Given f(x)=-3sec(2x), find f^(')(x). Answer: f^(')(x)=

Recall Secant Derivative: Recall the derivative of the secant function. The derivative of sec(u) with respect to x is sec(u)tan(u) times the derivative of u with respect to x (chain rule).Apply Chain Rule: Apply the chain rule to find the derivative of f(x) = -3sec(2x). Let u = 2x, then the derivative of u with respect to x is du/dx = 2. The derivative of f(x) with respect to x is then f'(x) = -3 * d/dx[sec(u)] * du/dx.Calculate Derivative: Calculate the derivative using the result from Step 1. f'(x) = -3 * sec(u)tan(u) * 2 Since u = 2x, we substitute back to get: f'(x) = -3 * sec(2x)tan(2x) * 2Simplify Expression: Simplify the expression for the derivative. f'(x) = -6 * sec(2x)tan(2x) This is the derivative of f(x) with respect to x.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given
f(x)=-3sec(2x), find
f^(')(x).
Answer:
f^(')(x)=

Given $f(x)=-3 \sec (2 x)$ , find $f^{\prime}(x)$ . $\newline$ Answer: $f^{\prime}(x)=$

View step-by-step help

Home

Math Problems

Algebra 2

Transformations of absolute value functions

Full solution

Q. Given

f(x)=-3 \sec (2 x)

, find

f^{\prime}(x)

\newline

Answer:

f^{\prime}(x)=

Recall Secant Derivative: Recall the derivative of the secant function. The derivative of $\sec(u)$ with respect to $x$ is $\sec(u)\tan(u)$ times the derivative of $u$ with respect to $x$ (chain rule).
Apply Chain Rule: Apply the chain rule to find the derivative of $f(x) = -3\sec(2x)$ . Let $u = 2x$ , then the derivative of $u$ with respect to $x$ is $\frac{du}{dx} = 2$ . The derivative of $f(x)$ with respect to $x$ is then $f'(x) = -3 \cdot \frac{d}{dx}[\sec(u)] \cdot \frac{du}{dx}$ .
Calculate Derivative: Calculate the derivative using the result from Step $1$ . $\newline$ $f'(x) = -3 \times \sec(u)\tan(u) \times 2$ $\newline$ Since $u = 2x$ , we substitute back to get: $\newline$ $f'(x) = -3 \times \sec(2x)\tan(2x) \times 2$
Simplify Expression: Simplify the expression for the derivative. $\newline$ $f'(x) = -6 \cdot \sec(2x)\tan(2x)$ $\newline$ This is the derivative of $f(x)$ with respect to $x$ .