Elleanor Mckenzie

2021-04-30

Derivatives of the sum of functions Find the derivative of the following functions.
$f\left(x\right)=3{x}^{4}+7x$

timbalemX

Step 1
We have to find the derivatives of following function:
We know the formula of derivatives,
$\frac{{dx}^{n}}{dx}=n{x}^{n-1}$ (power rule)
$\frac{da{x}^{n}}{dx}=a\frac{{dx}^{n}}{dx}$ (where a is some constant)
$\frac{dx}{dx}=1$
$\frac{d\left(cons\mathrm{tan}t\right)}{dx}=0$
$\frac{df\left(x\right)}{dx}={f}^{\prime }\left(x\right)$
$\frac{dg\left(x\right)}{dx}={g}^{\prime }\left(x\right)$
Applying above formulae for the given functions:
Differentiating the given function with respect to 'x', we get
$\frac{df\left(x\right)}{dx}=\frac{d\left(3{x}^{4}+7x\right)}{dx}$
${f}^{\prime }\left(x\right)=3\frac{{dx}^{4}}{dx}+7\frac{dx}{dx}$
$=3\left(4{x}^{4-1}\right)+7×1$
$=12{x}^{3}+7$
Hence, derivative of the function is $12{x}^{3}+7$.

Jeffrey Jordon