Question

find the derivative of the following function. f(x)=13x^5 - 26x + e^5 f(x)=□

Explanation:

Step1: Apply power - rule to $13x^5$

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $y = 13x^5$, $a = 13$ and $n = 5$. So the derivative is $13\times5x^{5 - 1}=65x^{4}$.

Step2: Apply power - rule to $-26x$

For $y=-26x$, where $a=-26$ and $n = 1$. Using the power - rule $y^\prime=-26\times1x^{1 - 1}=-26$.

Step3: Derivative of a constant

The derivative of a constant $C$ is $0$. Since $e^5$ is a constant, its derivative is $0$.

Step4: Combine the derivatives

$f^\prime(x)$ is the sum of the derivatives of each term. So $f^\prime(x)=65x^{4}-26 + 0$.

Answer:

$65x^{4}-26$