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I have been asked to differentiate the following expression:

$$f(y)=\left(\frac{e^y}{2}\right)^4$$

the answer according to the worksheet is $\frac{e^{4y}}{y}$

however I cannot get to this point,

Any help would be greatly appreciated.

EDIT - Can someone also state whether the answer I have been given in the worksheet is correct?

  • 0
    Apply chain rule. $\frac{1}{16}*4*(e^y)^3*e^y$ – 2017-01-06
  • 0
    Okay, and what's your question? – 2017-01-06
  • 0
    The worksheet does not seem correct... – 2017-01-06

3 Answers 3

1

Hint: We can write $$f (y)=\frac {1}{16}e^{4y} $$ We now that $$\frac {d}{dx}(e^{ax}) =ae^{ax} $$ Use that fact to get $f'(y) $. Hope it helps.

2

Hint: $$f(y)=(\frac{1}{2}*e^y)^4=\frac{1}{16}e^{4y}$$

1

$$\frac{df}{dy} = {1\over 16} e^{4y} \frac{d}{dy} (4y) = \frac{e^{4y}}{4}$$