Differentiate the following with respect to x:
Question:

Differentiate the following with respect to x:

$\left(a x^{2}+b x+c\right)$

 

Solution:

To Find: Differentiation

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

$\frac{d(u \cdot v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

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

So, by using the above formula, we have

$\frac{d}{d x}\left(a x^{2}+b x+c\right)=2 a x+b$

Differentiation of $y=\left(a x^{2}+b x+c\right)$ is $2 a x+b$

 

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