In part 2 you need to use the chain rule.
When you differentiated you forgot to multiply by as per the chain rule.
Your expression at the end is actually equal to
I've got two derivatives, one is logarithmic.
Okay, here is the first one:
f(x) = ln (x^2 * e^2x) / (x + ln x)
I tried doing this and the problem exploded into this huge mess. I know there is a simpler way and in fact this problem is simpler than most problems given I just forget how to simplify this. The best I could do was
Numerator can = 1 / (x^2 * e^2x)
Denominator can = x + 1/x
From this however, the entire thing explodes using the appropriate rules. Isn't there some way to simplify this further?
Okay phew, part II. Using logarithmic differentiation
f(x) = (cos(x))^x
lny = ln(cos(x))^x
1/y = 1/ x cos(x)
1/y = x * -sin(x) / cos(x)
I kinda block here. I must multiply by y on both sides but then the left side is just a "1".
I get y/y = y * -sin(x) * x / cos(x)
The y on the right can then be substituted by the original y but what happens on the left side?