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 $-3 x^{2} \sin \left(x^{3}\right)$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.