Problem 14
Compute the derivative of the given function. $$f(x)=\cos (3 x)$$
Problem 14
An invertible function \(f(x)\) is given along with a point that lies on its graph. Using Theorem 2.7.1, evaluate \(\left(f^{-1}\right)^{\prime}(x)\) at the indicated value. \(f(x)=6 e^{3 x}\) Point \(=(0,6)\) Evaluate \(\left(f^{-1}\right)^{\prime}(6)\)
Problem 14
(a) Use the Quotient Rule to differentiate the function. (b) Manipulate the function algebraically and differentiate without the Quotient Rule. (c) Show that the answers from \((\mathrm{a})\) and \((\mathrm{b})\) are equivalent. $$f(t)=\frac{t^{2}-1}{t+1}$$
Problem 14
Find \(\frac{d y}{d x}\) using implicit differentiation. $$x^{2 / 5}+y^{2 / 5}=1$$
Problem 14
Compute the derivative of the given function. $$f(\theta)=9 \sin \theta+10 \cos \theta$$
Problem 14
Use the definition of the derivative to compute the derivative of the given function. $$r(s)=\frac{1}{s-2}$$
Problem 15
Compute the derivative of the given function. $$f(x)=x \sin x$$
Problem 15
Compute the derivative of the given function. $$f(r)=6 e^{r}$$
Problem 15
Compute the derivative of the given function. $$h(t)=\sin ^{-1}(2 t)$$
Problem 15
Find \(\frac{d y}{d x}\) using implicit differentiation. $$\cos (x)+\sin (y)=1$$
