Question

differentiate y=ax^2+b sin x (a and b are constant)​

Answer 1

Given :

Function :

$\sf\:y=ax{}^{2}+b\sin\:x$

To find :

$\dfrac{dy}{dx}$

Formulas Used :

$1) \dfrac{d(sinx)}{dx} = cosx$

$2) \dfrac{d(x {}^{n}) }{dx} = nx {}^{n - 1}$

$3) \dfrac{d(constant)}{dx} = 0$

Solution :

$\sf\:y=ax{}^{2}+b\sin\:x$

Differnatiate with respect to x

$\implies \dfrac{dy}{dx} = a \dfrac{d(x {}^{2}) }{dx} + b \dfrac{d (\sin x)}{dx}$

$\implies \dfrac{dy}{dx} = 2ax + b \cos x$

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More About Differention:

1) Every differentiable function is continuous but the converse is not true

2) A function is said to be differentiable in (a,b) , if it is differentiable at every point of (a,b)