f'(x)=

jernplate8
2021-11-10
Answered

Write the formula for the derivative of the function.

$f\left(x\right)=12{x}^{4}+19{x}^{3}+9$

f'(x)=

f'(x)=

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Nathanael Webber

Answered 2021-11-11
Author has **117** answers

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)

$f\left(x\right)=12{x}^{4}+19{x}^{3}+9$

${f}^{\prime}\left(x\right)=\frac{d}{dx}(12{x}^{4}+19{x}^{3}+9)$

$=12\frac{d}{dx}\left({x}^{4}\right)+19\frac{d}{dx}\left({x}^{3}\right)+0(n=0)$

$=48{x}^{3}+57{x}^{2}$

To differentiate the given functions

Step 2

Basic rule for differentiating powers of x

Basic rule:

Step 3

Apply the basic rule to both functions (recall, derivative of sum is sum of derivatives)

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