# a) Find the derivative of f(x)=(2x+9)(8x−7) by first expanding the polynomials.

a) Find the derivative of $$f(x)=(2x+9)(8x−7)$$ by first expanding the polynomials.
b) Find the derivative of $$f(x)=(2x+9)(8x−7)$$ by using the product rule. Let $$\displaystyle g{{\left({x}\right)}}={2}{x}+{9}{\quad\text{and}\quad}{h}{\left({x}\right)}={8}{x}-{7}$$

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Leonard Stokes

a) $$f(x)=(2x+9)(8x-7)$$
$$\displaystyle{f{{\left({x}\right)}}}={16}{x}^{{2}}-{14}{x}+{72}{x}-{63}$$
$$\displaystyle{f{{\left({x}\right)}}}={16}{x}^{{2}}+{58}{x}-{63}$$
$$\displaystyle{f}'{\left({x}\right)}={32}{x}+{58}$$
b) $$\displaystyle{f{{\left({x}\right)}}}={\left({2}{x}+{9}\right)}{\left({8}{x}-{7}\right)}$$
$$\displaystyle{g{{\left({x}\right)}}}={\left({2}{x}+{9}\right)}$$
$$\displaystyle{h}{\left({x}\right)}={8}{x}-{7}$$
$$\displaystyle{g}'{\left({x}\right)}={2}$$
$$\displaystyle{h}'{\left({x}\right)}={8}$$
$$\displaystyle{f{{\left({x}\right)}}}={\left({2}{x}+{9}\right)}{\left({8}{x}-{7}\right)}={g{{\left({x}\right)}}}\cdot{h}{\left({x}\right)}$$
$$\displaystyle{f}'{\left({x}\right)}={g{{\left({x}\right)}}}\cdot{h}'{\left({x}\right)}+{h}{\left({x}\right)}\cdot{g}'{\left({x}\right)}$$
$$\displaystyle{f}'{\left({x}\right)}={\left({2}{x}+{9}\right)}{\left({8}\right)}+{\left({8}{x}-{7}\right)}{\left({2}\right)}$$
$$\displaystyle{f}'{\left({x}\right)}={16}{x}+{72}+{16}{x}-{14}$$
$$\displaystyle{f}'{\left({x}\right)}={32}{x}-{58}$$