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Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$(3-4 x)^{5}$

 

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: $\frac{d}{d x}\left(y^{n}\right)=n y^{n-1} \times \frac{d y}{d x}$

Let us take $y=(3-4 x)^{5}$

So, by using the above formula, we have

$\frac{d}{d x}(3-4 x)^{5}=4(3-4 x)^{5} \times \frac{d}{d x}(3-4 x)=4(3-4 x)^{5} \times(-4)=-16(3-4 x)^{5}$

Differentiation of $y=(3-4 x)^{5}$ is $-16(3-4 x)^{5}$

 

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