Question

use the rules of differentiation to find the derivative of the function. h(x) = \frac{3}{x}-17\sec(x) h(x) =

Explanation:

Step1: Rewrite the function

Rewrite $\frac{3}{x}$ as $3x^{-1}$. So $h(x)=3x^{-1}-17\sec(x)$.

Step2: Apply the power - rule and the derivative of secant

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$, and the derivative of $\sec(x)$ is $\sec(x)\tan(x)$.
The derivative of $3x^{-1}$ is $3\times(-1)x^{-1 - 1}=-3x^{-2}=-\frac{3}{x^{2}}$, and the derivative of $- 17\sec(x)$ is $-17\sec(x)\tan(x)$.

Step3: Combine the derivatives

$h^\prime(x)=-\frac{3}{x^{2}}-17\sec(x)\tan(x)$.

Answer:

$-\frac{3}{x^{2}}-17\sec(x)\tan(x)$