- #1
Dr Zoidburg
- 39
- 0
Help please on these. I'm extremely rusty with differentiation and want to know if I've got the right answers here
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
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.
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
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.