Question

Find f’(2) for f(x)=5e^-xln(x^2+5x)

Answer 1

9514 1404 393

Answer:

f'(2) ≈ −1.3508

Explanation:

The derivative of the function is ...

f'(x) = 5(-e^-x·ln(x^2 +5x) +e^-x·(2x +5)/(x^2 +5x))

Then ...

f'(2) = 5e^(-2)(-ln(14) +9/14) ≈ -1.3508