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Find the derivative of the following functions (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\left( {{x^2} + 1} \right)\cos x$.
Find the derivative of the following functions (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\left( {{x^2} + 1} \right)\cos x$.
CBSE | Class 11 | Limits and Derivatives | Maths | Miscellaneous Exercise | NCERT
Find the derivative of the following functions (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\left( {{x^2} + 1} \right)\cos x$.

Assume, $f(x) = \left( {{x^2} + 1} \right)\cos x$.

Upon differentiating with respect to $x$ and applying quotient rule we get,

${f^\prime }(x) = \left( {{x^2} + 1} \right)\frac{d}{{dx}}(\cos x) + \cos x\frac{d}{{dx}}\left( {{x^2} + 1} \right)$

$f'(x) = \left( {{x^2} + 1} \right)( – \sin x) + \cos x(2x)$

Therefore, $f'(x) =  – {x^2}\sin x – \sin x + 2x\cos x$.

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