Derivatives of the sum of functions Find the derivative of the following functions. f(x)=3x4+7x

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

Answer is given below (on video)