Exercise 11.8 Archives - Noon Academy

Exercise 11.8

Differentiate $\sin ^{2} x$ with respect to $e^{\cos x}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{1-x}{1+x}\right)$ with respect to $\sqrt{1-x^{2}}$ , if $-1<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(2 a x \sqrt{1-a^{2} x^{2}}\right)$ with respect to $\sqrt{1-a^{2} x^{2}}$ , if $-\frac{1}{\sqrt{2}}<a x<\frac{1}{\sqrt{2}}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1} \sqrt{1-x^{2}}$ with respect to $\cot ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)$ , if $0<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)$ with respect to $\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ , if $-\frac{1}{\sqrt{2}}<x<\frac{1}{\sqrt{2}}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\cos ^{-1}\left(4 x^{3}-3 x\right)$ with respect to $\tan ^{-1}\left(\frac{\sqrt{1-x^{2}}}{x}\right)$ , if $\frac{1}{2}<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$ with respect to $\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)$ , if $-1<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right)$ with respect to $\sec ^{-1} x$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{x-1}{x+1}\right)$ with respect to $\sin ^{-1}\left(3 x-4 x^{3}\right)$ , if $-\frac{1}{2}<x<\frac{1}{2}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ , if $0<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ with respect to $\tan ^{-1}\left(\frac{x}{\sqrt{1-x^{2}}}\right)$ , if $-\frac{1}{\sqrt{2}}<x<\frac{1}{\sqrt{2}}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{1+a x}{1-a x}\right)$ with respect to $\sqrt{1+a^{2} x^{2}}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ , if $0<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $(\cos x)^{\sin x}$ with respect to $(\sin x)^{\cos x}$ .

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question, ......(i) ........(ii)

Differentiate $\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ with respect to $\sec ^{-1}\left(\frac{1}{\sqrt{1-x^{2}}}\right)$ , if $x \in\left(\frac{1}{\sqrt{2}}, 1\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ with respect to $\sec ^{-1}\left(\frac{1}{\sqrt{1-x^{2}}}\right)$ , if $x \in\left(0, \frac{1}{\sqrt{2}}\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\tan ^{-1}\left(\frac{\sqrt{1+x^{2}}-1}{x}\right)$ with respect to $\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$ , if $-1<x<1, x \neq 0$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(4 x \sqrt{1-4 x^{2}}\right)$ with respect to $\sqrt{1-4 x^{2}}$ , if $x \in\left(-\frac{1}{2},-\frac{1}{2 \sqrt{2}}\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(4 x \sqrt{1-4 x^{2}}\right)$ with respect to $\sqrt{1-4 x^{2}}$ , if $x \in\left(\frac{1}{2 \sqrt{2}}, \frac{1}{2}\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1}\left(4 x \sqrt{1-4 x^{2}}\right)$ with respect to $\sqrt{1-4 x^{2}}$ , if $x \in\left(\frac{1}{-2 \sqrt{2}}, \frac{1}{2 \sqrt{2}}\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1} \sqrt{1-x^{2}}$ with respect to $\cos ^{-1} x_{1}$ if $x \in(-1,0)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sin ^{-1} \sqrt{1-x^{2}}$ with respect to $\cos ^{-1} x$ , if $x \in(0,1)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $(\log x)^{x}$ with respect to $\log x$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\log \left(1+x^{2}\right)$ with respect to $\tan ^{-1} x$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

Differentiate $\sec ^{2}\left(x^{2}\right)$ with respect to $x^{2}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

As per the given question,

$\text { Dif ferentiate } \tan ^{-1}\left(\frac{1+a x}{1-a x}\right) \text { with respect to } \sqrt{1+a^{2} x^{2}} \text {. }$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

$\text { Dif ferentiate } \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \text { with respect to } \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right), \text { if } 0<x<1$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

$\text { Differentiate }(\cos x)^{\sin x} \text { with respect to }(\sin x)^{\cos x} .$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

Differentiate $\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ with respect to $\sec ^{-1}\left(\frac{1}{\sqrt{1-x^{2}}}\right)$ , if, (i) $x \in(0,1 / \sqrt{2})$ (ii) $x \in(1 / \sqrt{2}, 1)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

(i) Let (ii) Let

$\text { Differentiate } \tan ^{-1}\left(\frac{\sqrt{1+x^{2}}-1}{x}\right) \text { with respect to } \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), \text { if }-1<x<1, x \neq 0 \text {. }$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

Differentiate $\sin ^{-1}\left(4 x \sqrt{1-4 x^{2}}\right)$ with respect to $\sqrt{1-4 x^{2}}$ if, (iii) $x \epsilon\left(-\frac{1}{2},-\frac{1}{2 \sqrt{2}}\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

(iii) Let

Differentiate $\sin ^{-1}\left(4 x \sqrt{1-4 x^{2}}\right)$ with respect to $\sqrt{1-4 x^{2}}$ if, (i) $x \epsilon\left(-\frac{1}{2 \sqrt{2}}, \frac{1}{2 \sqrt{2}}\right)$ (ii) $x \in\left(\frac{1}{2 \sqrt{2}}, \frac{1}{2}\right)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

(i) Let (ii)

Differentiate $\sin ^{-1} \sqrt{\left(1-x^{2}\right)}$ with respect to $\cos ^{-1} x$ , if (i) $x \in(0,1)$ (ii) $x \in(-1,0)$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

(i) Given sin-1 √ (1-x2) (ii) Given sin-1 √ (1-x2)

$\text { Differentiate }(\log x)^{\mathrm{x}} \text { with respect to } \log \mathrm{x} \text {. }$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

$\text { Differentiate } \log \left(1+x^{2}\right) \text { with respect to } \tan ^{-1} x$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma

$\text { Differentiate } \mathbf{x}^{2} \text { with respect to } \mathrm{x}^{3}$

CBSE, Class 12, Differentiation, Exercise 11.8, Maths, RD Sharma