# Calculate the derivatives of the functions. Then find the values of the derivatives as specified. f(x)=4-x^{2}; f'(-3),f'(0),f'(1)

Calculate the derivatives of the functions. Then find the values of the derivatives as specified.
$$\displaystyle{f{{\left({x}\right)}}}={4}-{x}^{{{2}}};{f}'{\left(-{3}\right)},{f}'{\left({0}\right)},{f}'{\left({1}\right)}$$

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Step 1
Given function
$$\displaystyle{f{{\left({x}\right)}}}={4}-{x}^{{{2}}}$$
To find the derivative , the derivative given below is used
$$\displaystyle{f}'{\left({x}^{{{n}}}\right)}={n}{x}^{{{n}-{1}}}$$
So the derivative of given function is
$$\displaystyle{f}'{\left({x}\right)}=-{2}{x}$$
Step 2
The values of specified derivatives are
$$\displaystyle{f}'{\left({x}\right)}=-{2}{x}$$
$$\displaystyle{f}'{\left(-{3}\right)}=-{2}\times-{3}$$
=6
$$\displaystyle{f}'{\left({0}\right)}=-{2}\times{0}$$
=0
$$\displaystyle{f}'{\left({1}\right)}=-{2}\times{1}$$
=-2