Question

If f(x)=e^2x(x^3+1) then f'(2)=

Answer 1

Answer:

See below

Step-by-step explanation:

$f(x)=e^2x(x^3+1) = e^2x^4+x$

Considering

$f'(x)=\dfrac{d}{dx}f(x)=\dfrac{d}{dx}e^2x^4+\dfrac{d}{dx}x$

Once the derivative of a constant is 1 and  $e^x = \dfrac{d}{dx} e^x$

Then,

$\dfrac{d}{dx}f(x)=\dfrac{d}{dx}e^2x^4+\dfrac{d}{dx}x =\boxed{ e^2 4x^3+1}$

Therefore,

$f'(2) = e^24\cdot 2^3 +1 = 32e^2+1$