91Ó°ÊÓ

Use logarithmic differentiation to find \(\frac{d y}{d x}\). $$ y=\frac{x+11}{\sqrt[3]{x^{2}-4}} $$

For the following exercises, use logarithmic differentiation to find \(\frac{d y}{d x}\) $$y=\frac{x+11}{\sqrt[3]{x^{2}-4}}$$

Use logarithmic differentiation to find \(\frac{d y}{d x}\). $$ y=x^{-1 / 2}\left(x^{2}+3\right)^{2 / 3}(3 x-4)^{4} $$

For the following exercises, use logarithmic differentiation to find \(\frac{d y}{d x}\) $$y=x^{-1 / 2}\left(x^{2}+3\right)^{2 / 3}(3 x-4)^{4}$$

Find an equation of the tangent line to the graph of \(f(x)=4 x e^{\left(x^{2}-1\right)}\) at the point where \(x=-1\). Graph both the function and the tangent line.

[T] Find an equation of the tangent line to the graph of \(f(x)=4 x e^{\left(x^{2}-1\right)}\) at the point where \(x=-1 .\) Graph both the function and the tangent line.

Find the equation of the line that is normal to the graph of \(f(x)=x \cdot 5^{x}\) at the point where \(x=1\). Graph both the function and the normal line.

[T] Find the equation of the line that is normal to the graph of \(f(x)=x \cdot 5^{x}\) at the point where \(x=1 .\) Graph both the function and the normal line.

Find the equation of the tangent line to the graph of \(x^{3}-x \ln y+y^{3}=2 x+5\) at the point where \(x=2\). (Hint: Use implicit differentiation to find \(\frac{d y}{d x}\).) Graph both the curve and the tangent line.

[T] Find the equation of the tangent line to the graph of \(x^{3}-x \ln y+y^{3}=2 x+5\) at the point where \(x=2\) . (Hint: Use implicit differentiation to find \(\frac{d y}{d x} .\) ) Graph both the curve and the tangent line.