Need help with number 5,6,& 7 please!! Thank you!
5a) Use the chain rule.
$\displaystyle (uv)'=u'v+uv'$
5b) Use the chain rule. For logarithmic differentiation, you the formula $\displaystyle \log_a x=\frac {\ln x}{\ln a}$
5c) $\displaystyle (\ln |x|)'=\frac {x'}{x}$, so $\displaystyle \frac {1}{(\cos ^2e^{-x})(\tan (e^{-x}))}$
6) Rewrite for y. For example, $\displaystyle x=e^y, y=\ln x$ Use the tangent line formula. Given the coordinate (a, f(a)), the equation of the tangent line is y-f(a)=f'(a)(x-a)
6b)Same thing
7) Find the derivative, and set y'=0 and solve that equation. The solutions you get for y'=0, sub that into y, and you'll find out the local extremas.
This is not calculus 3. This is calculus 1, just very difficult calculus 1 problems.