SOLUTION: Find f ’(x) if f(x) = 5 tan(x) - 2 e^x - 3 and evaluate f ’(1). (Keep 2 decimal places)

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Question 1016416: Find f ’(x) if
f(x) = 5 tan(x) - 2 e^x - 3
and evaluate f ’(1). (Keep 2 decimal places)
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find f ’(x) if
f(x) = 5 tan(x) - 2 e^x - 3
and evaluate f ’(1). (Keep 2 decimal places)
----------------------------------------------------- 

f(x) = 5%2Atan%28x%29+-+2e%5Ex+-+3

You probably know that (tan(x))' = 1%2Fcos%5E2%28x%29 

                       (e%5Ex)' = e%5Ex.

Therefore,

f'(x) = 5%2Fcos%5E2%28x%29 - 2e%5Ex.


Hence, f'(1) = 5%2Fcos%5E2%281%29 - 2e%5E1 = 5%2Fcos%5E2%281%29 - 2e.

Please calculate it yourself.

You need to know the table for basic derivatives.
See, for example, http://www.math.ubc.ca/~feldman/m200/formulae.pdf.