Home > Calculus > Differentiating Exponential Functions with Base e

How do you find the derivative of #y=e^(2x^2+2x)#?

Answer 1

#d/dxe^(2x^2+2x)=(4x+2)e^(2x^2+2x)#

This problem will require an application of the Chain Rule which, when applied to #e# raised to the power of some function #u,# tells us that

#d/dxe^u=e^u*(du)/dx#

Here, #u=2x^2+2x,# so we have

#d/dxe^(2x^2+2x)=e^(2x^2+2x)*d/dx(2x^2+2x)#

#d/dx(2x^2+2x)=4x+2#, so we end up with

#d/dxe^(2x^2+2x)=(4x+2)e^(2x^2+2x)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emily Ammerman

To find the derivative of ( y = e^{2x^2+2x} ), you can use the chain rule. The derivative is ( y' = e^{2x^2+2x} \cdot (4x + 2) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.