91Ó°ÊÓ

Find \(d^{2} y / d x^{2}\). $$y=x^{4}-7$$

Differentiate each function. $$y=(3-2 x)^{2}$$ Check by expanding and then differentiating.

Differentiate two ways: first, by using the Product Rule; then, by multiplying the expressions before differentiating. Compare your results as a check. $$y=x^{9} \cdot x^{4}$$

Find \(\frac{d y}{d x}\). $$y=x^{8}$$

In Exercise : a) Graph the function. b) Draw tangent lines to the graph at points whose \(x\) -coordinates are \(-2,0,\) and 1. c) Find \(f^{\prime}(x)\) by determining \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}.\) d) Find \(f^{\prime}(-2), f^{\prime}(0),\) and \(f^{\prime}(1) .\) These slopes should match those of the lines you drew in part ( \(b\) ). $$f(x)=-2 x^{2}$$

Find \(\frac{d y}{d x}\). $$y=-3 x$$

Differentiate each function. $$y=(7-x)^{55}$$

Differentiate two ways: first, by using the Product Rule; then, by multiplying the expressions before differentiating. Compare your results as a check. $$f(x)=(2 x+5)(3 x-4)$$

Find \(d^{2} y / d x^{2}\). $$y=2 x^{4}-5 x$$

In Exercise : a) Graph the function. b) Draw tangent lines to the graph at points whose \(x\) -coordinates are \(-2,0,\) and 1. c) Find \(f^{\prime}(x)\) by determining \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}.\) d) Find \(f^{\prime}(-2), f^{\prime}(0),\) and \(f^{\prime}(1) .\) These slopes should match those of the lines you drew in part ( \(b\) ). $$f(x)=-3 x^{2}$$