Question

find the derivative of the following function. f(x)=2x^{3}+5x f(x)=□

Explanation:

Step1: Apply power - rule to first term

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the term $2x^3$, where $a = 2$ and $n = 3$, the derivative is $2\times3x^{3 - 1}=6x^2$.

Step2: Apply power - rule to second term

For the term $5x$, where $a = 5$ and $n = 1$, using the power - rule $y^\prime=anx^{n - 1}$, we get $5\times1x^{1 - 1}=5$.

Step3: Sum the derivatives

Since the derivative of a sum of functions $f(x)=u(x)+v(x)$ is $f^\prime(x)=u^\prime(x)+v^\prime(x)$, for $u(x)=2x^3$ and $v(x)=5x$, we have $f^\prime(x)=6x^2 + 5$.

Answer:

$6x^2+5$