Question

differentiate cos(x^5.e^x)​

Answer 1

Answer:

The answer is $-e^x\sin(x^5e^x)(x^5+5x^4)$

Step-by-step explanation:

Let $y=\cos(x^5e^x)$

Using chain rule of differentiation

$\dfrac{dy}{dx}=\dfrac{d}{dx}[\cos(x^5e^x)]$

     $=-\sin(x^5e^x)\dfrac{d}{dx}(x^5e^x)\\=-\sin(x^5e^x)[x^5\dfrac{d}{dx}e^x+e^x\dfrac{d}{dx}(x^5)]\\\\=-\sin(x^5e^x)(x^5e^x+e^x(5x^4))\\\\=-e^x\sin(x^5e^x)(x^5+5x^4)$