Home > Calculus > Differentiating Exponential Functions with Base e

What is the derivative of #e^(x^2)#?

Answer 1

Christopher Allers

#d/dxe^(x^2)=2xe^(x^2)#

In general, when applying the Chain Rule to the exponential,

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

Here, #u=x^2,# so

#d/dxe^(x^2)=e^(x^2)d/dxx^2#

#d/dxe^(x^2)=2xe^(x^2)#

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Answer 2

Isabella Ackerman

The derivative of ( e^{x^2} ) is ( 2x e^{x^2} ).

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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.

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