Just wondering if I have done this correctly?
Homework Statement
Differentiate:
x^{sin3x}
The Attempt at a Solution
x^{sin3x}=e^{sin(3x)ln(x)
Employing chain rule.
y=e^{u}
u=sin(3x)ln(x)
dy/dx = e^{u}\times(sin(3x)/x + 3ln(x)cos(3x))
Final Solution? =
dy/dx =...
It's a basic calculus problem for some uni homework, but it's been a while and I'm rusty.
More or less just looking for a check on my work
Homework Statement
Differentiate:
v(t)= 6e^(-t).ln(t+5)
The Attempt at a Solution
Using the product rule:
v'(t) = du/dt(6e^(-t)).ln(t+5)...
I'm working on a Maths assignment and one of the problem solving questions is to prove:
\int cos^{8}(x)dx=\frac{1}{8}cos^{7}(x).sin(x)+\frac{7}{48}cos^{5}(x).sin(x)+\frac{35}{192}cos^{3}(x).sin(x)+\frac{35}{128}cos(x).sin(x)+\frac{35}{128}(x)+c
I have looked through my textbook and found a good...