am trying to differentiate these equations
$\displaystyle y = tan^2(x)^3 + cos 2x$ and
$\displaystyle y=(e^x)^2/ln(2x)$
U substitution is a topic for integration, not differentiation. If you can show us your work, we will be more than happy to help point you in the right direction.
You may also want to check out this link, which covers product, quotient and chain rules for differentiation: Product Rule, Quotient Rule, and Chain Rule Tutorial
Just in case a picture helps...
... where
... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).
Spoiler:
________________________________________
Don't integrate - balloontegrate!
Balloon Calculus: Standard Integrals, Derivatives and Methods
Balloon Calculus Drawing with LaTeX and Asymptote!
1. the derivative of $\displaystyle tan^{2}(x)^3 = 2tan(x^3)sec^2(x^3) 3x^2$
Likewise find out the derivaitve of $\displaystyle cos2x$ and add them up
2. try the quotient rule, show how much effort you put on this problem. Post if you have any errors and they will be fixed.
I'll help you a bit with the first one to get you started
$\displaystyle y = tan^2(x)^3 + cos 2x$
Now let $\displaystyle p = tan^2(x)^3, q = cos2x$
We want Y` so
$\displaystyle y` = p` + q`$
This makes it easy, all we need to do is differentiate P and Q seperately and then add them up!
Well Q` is fairly easy
$\displaystyle q` = -2sin2x $
I leave $\displaystyle tan^2(x)^3$ to you. But I would like to let you know that
$\displaystyle Tan^2x = Sin^2x/Cos^2x $
This might make it easiar to apply quotient rule?