Problem 35
An implicitly defined function is given. Find \(\frac{d^{2} y}{d x^{2}} .\) Note: these are the same problems used in Exercises 13 through 16. $$\cos x+\sin y=1$$
Problem 35
Find the equations of the tangent and normal lines to the graph of the function at the given point. \(g(x)=\ln x\) at \(x=1\).
Problem 35
Compute the derivative of the given function. $$f(x)=\frac{\sin (4 x+1)}{(5 x-9)^{3}}$$
Problem 35
A function \(f(x)\) is given, along with its domain and derivative. Determine if \(f(x)\) is differentiable on its domain. \(f(x)=\sqrt{x^{5}(1-x)},\) domain \(=[0,1], f^{\prime}(x)=\frac{(5-6 x) x^{3 / 2}}{2 \sqrt{1-x}}\)
Problem 35
Compute the derivative of the given function. $$f(x)=x^{2} e^{x} \tan x$$
Problem 36
A function \(f(x)\) is given, along with its domain and derivative. Determine if \(f(x)\) is differentiable on its domain. \(f(x)=\cos (\sqrt{x}),\) domain \(=[0, \infty), f^{\prime}(x)=-\frac{\sin (\sqrt{x})}{2 \sqrt{x}}\)
Problem 36
Compute the derivative of the given function. $$f(x)=\frac{(4 x+1)^{2}}{\tan (5 x)}$$
Problem 36
An implicitly defined function is given. Find \(\frac{d^{2} y}{d x^{2}} .\) Note: these are the same problems used in Exercises 13 through 16. $$\frac{x}{y}=10$$
Problem 36
Compute the derivative of the given function. $$g(x)=2 x \sin x \sec x$$
Problem 36
Find the equations of the tangent and normal lines to the graph of the function at the given point. \(f(x)=4 \sin x\) at \(x=\pi / 2\).
