Question

differentiate

help pls


no spam​

Answer 1

Answer:

$\underline{\text{Formulas to be known:}}\\\\1.\:\dfrac{d}{dx} (x^n) = n.x^{n-1}\\\\2.\: \dfrac{d}{dx} (sin\:x) = cos\:x\\\\3.\;\dfrac{d}{dx}(e^x) = e^x$

We also know differentiation of two or more terms in addition can be done separately. Hence separating the terms we get:

$\implies \dfrac{d}{dx}\:(x^2+3x)^{15} + \dfrac{d}{dx}\:(sin\:(3x+2)) + \dfrac{d}{dx}\:[e^{(x^2 - 2x)}]\\\\\\\implies \dfrac{d}{dx}\: (x^2+3x)^{15} = 15.(x^2 + 3x)^{14} . ( 2x + 3 )\:\:\:...(1)\\\\\\\implies \dfrac{d}{dx}\:(sin\:(3x+2)) = cos\:(3x+2).(3) = 3.cos\:(3x + 2 )\:\:\:...(2)\\\\\\\implies \dfrac{d}{dx}\:(e^{(x^2-2x)}) = (e^{(x^2-2x)}) . ( 2x - 2)\:\:\:...(3)$

Hence differentiation of the question is: (1) + (2) + (3)

$\implies f'(x) = 15.(x^2+3x)^{14}.(2x+3) + 3.cos\:(3x+2) + e^{(x^2 - 2x)}.(2x - 2)$

This is the required answer.