How do you differentiate the equation?

e^x(x^3 + 2x) = f(x)

2 Answers
Oct 10, 2017

f'(x) = (e^x)(x^3+2x + 3x^2 + 2)

Explanation:

Step 1) You know that you must use the product rule because you are trying to find the derivative of a product.

Step 2) So, you do the derivative of the first (e^x) times the second (x^3+2x), plus the first (e^x) times the derivative of the second (x^3+2x).

f'(x) = d/dx(e^x)(x^3+2x) + (e^x)d/dx(x^3+2x)

Step 3) Now you must find simplify and find each derivative.

Step 4) The derivative of e^x is always e^x, and the derivative of (x^3+2x) is (3x^2 + 2). Insert those into the equation.

f'(x) = (e^x)(x^3+2x) + (e^x)(3x^2 + 2)

Step 5) Pull out the e^x, giving you your final answer.

f'(x) = (e^x)(x^3+2x + 3x^2 + 2)

Oct 10, 2017

d/dx(e^x(x^3+2x))=e^x(x^3+2x)+e^x(3x^2+2)

Explanation:

Apply the product rule: d/dx(f*g)=(f'*g)+(f*g')

Let f=e^x and g=x^3+2x

d/dx(e^x(x^3+2x))=d/dx(e^x)(x^3+2x)+(e^x)(d/dx(x^3+2x))

=e^x(x^3+2x)+e^x(3x^2+2)