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Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$\sin 4 x$

Solution:

To Find: Differentiation

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

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

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

Let us take y = sin 4x.

So, by using the above formula, we have

$\frac{d}{d x}(\sin 4 x)=\cos (4 x) \times \frac{d}{d x}(4 x)=4 \cos 4 x$

Differentiation of y = sin 4x is 4cos4x