SOLUTION: f(x)= 10e^x-ex^e. Find f'(3)

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Question 1180615: f(x)= 10e^x-ex^e. Find f'(3)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+10e%5Ex-e%2Ax%5Ee
Find f'%283%29
first find f'%28x%29

%28d%2Fdx%29%2810e%5Ex-e%2Ax%5Ee%29.......apply the Sum/Difference Rule
=%28d%2Fdx%29%2810e%5Ex%29-%28d%2Fdx%29%28e%2Ax%5Ee%29....factor constant out
=10%28d%2Fdx%29%28e%5Ex%29-e%28d%2Fdx%29%28x%5Ee%29
=10e%5Ex-e%5E2%2Ax%5E%28e-1%29

f'%28x%29+=+10e%5Ex+-+e%5E2%2Ax%5E%28e+-+1%29
then
f'%283%29+=+10e%5E3+-+e%5E2%2A3%5E%28e+-+1%29
f'%283%29+=+152.05