SOLUTION: Let f(x)=3e^(5x) + sin(2x) (a) Find the derivatives of f up to the third order, f'(x), f''(x), f'''(x). (b) Hence, evaluate the values of the derivatives above at x=0, i.e. f'(0)

Question 228394: Let f(x)=3e^(5x) + sin(2x)
(a) Find the derivatives of f up to the third order, f'(x), f''(x), f'''(x).
(b) Hence, evaluate the values of the derivatives above at x=0, i.e. f'(0), f''(0), f'''(0).
Help with this would be much appreciated.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let f(x)=3e^(5x) + sin(2x)
(a) Find the derivatives of f up to the third order, f'(x), f''(x), f'''(x).
---
f'(x) = 15e^(5x) + 2cos(x)
f'(0) = 15+2 = 17
---------------------
f"(x) = 75e^(5x)-2sin(x)
f"(0) = 75-0 = 75
---------------------
f'''(x) = 375e^(5x)-2cos(x)
f'''(0) = 375-2 = 373
=============================================
(b) Hence, evaluate the values of the derivatives above at x=0, i.e. f'(0), f''(0), f'''(0).
=============================================
Cheers,
Stan H.
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