How do you differentiate e^(-10x)?

2 Answers
Jun 11, 2018

-10e^(-10x)

Explanation:

Given: e^(-10x).

Use the chain rule, which states that,

dy/dx=dy/(du)*(du)/dx

Let u=-10x,:.(du)/dx=-10.

Then, y=e^u,:.dy/(du)=e^u.

Combining, we get:

dy/dx=e^u*-10

=-10e^u

Substitute back u=-10x to get the final answer:

=-10e^(-10x)

Note:

A common fact in derivatives is that d/dx(e^(f(x)))=f'(x)e^(f(x)).

d/dx(e^(-10x))=-10*e^(-10x)

Explanation:

By the formula (d(e^u))/dx=e^u*(du)/dx

d/dx(e^(-10x))=e^(-10x)*(d(-10x))/dx

d/dx(e^(-10x))=e^(-10x)*(-10)

d/dx(e^(-10x))=-10*e^(-10x)

I hope the explanation is useful....God bless...