Question

How do you differentiate `f(x)= (xe^x+4)^3` using the chain rule.?

Answer 1

= `3e^x(x+1)(xe^x+4)^2` or some version of that

Explanation:

This is the chain rule.
`(xe^x+4)^3`
dy/dx = `3(xe^x+4)^2` x (derivative of the inside)

= `3(xe^x+4)^2` x (`x` x `e^x` + `e^x`)

= `3(xe^x+4)^2` x (`xe^x` +`e^x`)

= `3e^x(x+1)(xe^x+4)^2`