question\nfor the following equation, find $f(x)$.\n$f(x)=2x^{4}+4x^{3}-2$

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the term $2x^4$, its derivative is $2\times4x^{4 - 1}=8x^3$.

Step2: Differentiate the second term

For the term $4x^3$, using the power - rule, its derivative is $4\times3x^{3 - 1}=12x^2$.

Step3: Differentiate the constant term

The derivative of a constant $C$ (in this case $C=-2$) is 0.

Step4: Combine the derivatives

$f^\prime(x)$ is the sum of the derivatives of each term. So $f^\prime(x)=8x^3 + 12x^2+0$.

Answer:

$f^\prime(x)=8x^3 + 12x^2$