How do you find the fourth derivative of #e^(2x)#?

Answer 1

You can use the chain rule to find the first derivative of #e^(2x)# and differentiate iteratively

#(de^(2x))/dx = (de^(2x))/(d(2x)) * (d(2x))/dx = 2e^(2x)#
#(d^((2))e^(2x))/dx^2 =4e^(2x)#
#(d^((3))e^(2x))/dx^3 =8e^(2x)#
#(d^((4))e^(2x))/dx^4 =16e^(2x)#

In general it is easy to see that:

#(d^((n))e^(alpha x))/dx^n =alpha^n e^(alphax)#
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Answer 2

To find the fourth derivative of ( e^{2x} ), you apply the chain rule repeatedly. The derivative of ( e^{2x} ) with respect to ( x ) is ( 2e^{2x} ). The second derivative is ( 4e^{2x} ), the third derivative is ( 8e^{2x} ), and the fourth derivative is ( 16e^{2x} ). Therefore, the fourth derivative of ( e^{2x} ) is ( 16e^{2x} ).

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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.

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.

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.

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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