How do you differentiate the equation?

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

2 Answers

#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)#