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

Skilled2021-05-02Added 108 answers

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

$\frac{df\left(x\right)}{dx}=\frac{d(3{x}^{4}+7x)}{dx}$

$f}^{\prime}\left(x\right)=3\frac{{dx}^{4}}{dx}+7\frac{dx}{dx$

$=3\left(4{x}^{4-1}\right)+7\times 1$

$=12{x}^{3}+7$

Hence, derivative of the function is$12{x}^{3}+7$ .

We have to find the derivatives of following function:

We know the formula of derivatives,

Applying above formulae for the given functions:

Differentiating the given function with respect to 'x', we get

Hence, derivative of the function is

Jeffrey Jordon

Expert2022-01-31Added 2575 answers

Answer is given below (on video)