91Ó°ÊÓ

Using the Product Rule In Exercises \(5-10\) , use the Product Rule to find the derivative of the function. \(f(x)=x^{3} \cos x\)

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. $$y=(2 x-7)^{3}$$

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(y=5\left(2-x^{3}\right)^{4}\)

Finding a Derivative In Exercises \(5-20,\) find \(d y / d x\) by implicit differentiation. \(x^{2} y+y^{2} x=-2\)

Finding a Derivative In Exercises 7-26, use the rules of differentiation to find the derivative of the function. $$y=x^{12}$$

Finding the Slope of a Tangent Line In Exercises 9-14, find the slope of the tangent line to the graph of the function at the given point. $$g(x)=\frac{3}{2} x+1, \quad(-2,-2)$$

Moving Point In Exercises \(7-10,\) a point is moving along the graph of the given function at the rate \(d x / d t .\) Find \(d y / d t\) for the given values of \(x .\) $$\begin{array}{l}{y=\cos x ; \frac{d x}{d t}=4 \text { centimeters per secund }} \\ {\text { (a) } x=\frac{\pi}{6} \quad \text { (b) } x=\frac{\pi}{4} \quad \text { (c) } x=\frac{\pi}{3}}\end{array}$$

Using the Product Rule In Exercises \(5-10\) , use the Product Rule to find the derivative of the function. \(g(x)=\sqrt{x} \sin x\)

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(g(x)=3(4-9 x)^{5 / 6}\)

Finding a Derivative In Exercises 7-26, use the rules of differentiation to find the derivative of the function. $$y=\frac{1}{x^{5}}$$