Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$\cos ^{2}\left(x^{3}\right)$

 

Solution:

To Find: Differentiation

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

$\frac{\mathrm{d}(\mathrm{u}, \mathrm{v})}{\mathrm{dx}}=\mathrm{V} \frac{\mathrm{du}}{\mathrm{dx}}+\mathrm{u} \frac{\mathrm{dv}}{\mathrm{dx}}$

Formula used: $\frac{d}{d x}\left(\cos ^{a} n u\right)=a \cos ^{a}-1^{n} n \frac{d}{d x}(\cos n u) \frac{d}{d x}(n u)$

Let us take $y=\cos ^{2}\left(x^{3}\right)$

So, by using the above formula, we have

$\frac{d}{d x} \cos ^{2}\left(x^{3}\right)=2 \cos x^{3}\left(-\sin \left(x^{3}\right)\right) 3 x^{2}=-6 x^{2} \cos \left(x^{3}\right) \sin x^{3}$

Differentiation of $y=\cos ^{2}\left(x^{3}\right)$ is $-6 x^{2} \cos \left(x^{3}\right) \sin x^{3}$

 

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