I have the following two functions that I'm not compleately sure I'm solving correctly mainly what bugs me is $\log(x)$.
1st Function:
$$ f(x) = \sin(2x^2 - 3\log(x)) $$
I simply treated this as composed function and used the rule for said function to solve for it this way:
$$ f'(x) = \cos(2x^3 - 3\log(x)) \cdot 4x - \frac{1}{3\ln(x)} $$ Would this be correctly calculated derivative of said function ?
2nd Function:
$$ f(x) = x\log(x^5) \cdot \cos(2x - e^x)^2 $$
I am not fully sure how to solve this as a compositum first and then as two seperate functions so i did it this way:
$$ f'(x) = \left(\frac{1}{x\ln(x^5)} \right) \cdot \cos(2x - e^x)^2 + x\log(x^5) \cdot (-2\sin(2x -e^x)) $$
Thanks in advance.