Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$\cos x^{3}$

 

Solution:

To Find: Differentiation

NOTE : When 2 functions are in the product then we used product rule i.e

$\frac{d(u, v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

Formula used: $\frac{d}{d x}(\cos n u)=-\sin n u \frac{d}{d x}(n u)$ and $\frac{d x^{n}}{d x}=n x^{n-1}$

Let us take $y=\cos x^{3}$

So, by using the above formula, we have

$\frac{d}{d x} \cos x^{3}=-\sin \left(x^{3}\right) \times \frac{d}{d x}\left(x^{3}\right)=-3 x^{2} \sin \left(x^{3}\right)$

Differentiation of $y=\cos x^{3}$ is $-3 x^{2} \sin \left(x^{3}\right)$

 

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