Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$\left(3 x^{2}-x+1\right)^{4}$

 

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

Let us take $y=\left(3 x^{2}-x+1\right)^{4}$

So, by using the above formula, we have

$\frac{d}{d x}\left(3 x^{2}-x+1\right)^{4}=4\left(3 x^{2}-x+1\right)^{3} \times \frac{d}{d x}\left(3 x^{2}-x+1\right)=4\left(3 x^{2}-x+1\right)^{3} \times(3 \times 6 x-1)$

$=4\left(3 x^{2}-x+1\right)^{3}(6 x-1)$

Differentiation of $y=\left(3 x^{2}-x+1\right)^{4}$ is $4\left(3 x^{2}-x+1\right)^{3}(6 x-1)$

 

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