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How do I find the derivative of #y= arccos (e^7x)#?

Answer 1

Emily Ammerman

The answer is: #y'=-e^7/sqrt(1-e^14x^2#

The derivative of the function: #y=arccosf(x)# is

#y'=-1/(sqrt(1-[f(x)]^2))*f'(x)#.

So:

#y'=-1/sqrt(1-(e^7x)^2)*e^7=-e^7/sqrt(1-e^14x^2)#.

A common error is considering #e^n# as a function, but it is only a number! Remember that the function is #e^x#!

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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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