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

1 Answer
Jan 30, 2015

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#!