Question

find the derivative of the following function. f(x)=5x^3 - 29x + e^2 f(x)=□

Explanation:

Step1: Apply power - rule to $5x^3$

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $y = 5x^3$, $a = 5$ and $n = 3$. So the derivative is $5\times3x^{3 - 1}=15x^2$.

Step2: Apply power - rule to $-29x$

For $y=-29x$, $a=-29$ and $n = 1$. Using the power - rule $y^\prime=-29\times1x^{1 - 1}=-29$.

Step3: Derivative of a constant

The derivative of a constant $C$ is 0. Since $e^2$ is a constant, its derivative is 0.

Step4: Combine the derivatives

$f^\prime(x)$ is the sum of the derivatives of each term. So $f^\prime(x)=15x^2-29 + 0$.

Answer:

$15x^2-29$