# Write the formula for the derivative of the function. f(x)=12x^{4}+19x^{3}+9 f'(x)=

Write the formula for the derivative of the function.
$f\left(x\right)=12{x}^{4}+19{x}^{3}+9$
f'(x)=
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Step 1
To differentiate the given functions
Step 2
Basic rule for differentiating powers of x
Basic rule:
$\frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}$
Step 3
Apply the basic rule to both functions (recall, derivative of sum is sum of derivatives)
$f\left(x\right)=12{x}^{4}+19{x}^{3}+9$
${f}^{\prime }\left(x\right)=\frac{d}{dx}\left(12{x}^{4}+19{x}^{3}+9\right)$
$=12\frac{d}{dx}\left({x}^{4}\right)+19\frac{d}{dx}\left({x}^{3}\right)+0\left(n=0\right)$
$=48{x}^{3}+57{x}^{2}$