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**1. Homework Statement**

differentiate the following functions (you do not have to simplify):

a. f(x)=[tex](x-2)^{3}e^{-2x}[/tex]

b. f(x) = cos x / ln ([tex]x^{2}[/tex] + x)

c. g(t) = [tex]cos^{4}[/tex]([tex]t^{2} + e^{2t}[/tex])

d. f(x) = ln (h(x))

e. [tex]y = (sin x)^{ln x}[/tex] x>0

**3. The Attempt at a Solution**

First three I think I've got:

a. I used the product rule and came out with the following:

[tex]-6(x-2)^{2}e^{-2x}[/tex]

b. -([tex]x^{2}[/tex] + x) sin x / (2x + 1)

c. [tex]-8(t + e^{2t})cos^{3}(t^{2} + e^{2t})sin(t^{2} + e^{2t})[/tex]

d and e I'm stuck on! Should I use the Chain rule for d and e?

If a, b and/or c are wrong, any pointers would be awesome. cheers.