Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

Given f(x)=−3sec⁡(2x) f(x)=-3 \sec (2 x) , find f′(x) f^{\prime}(x) .\newlineAnswer: f′(x)= f^{\prime}(x)=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Transformations of absolute value functionsright chevron icon

Full solution

Q. Given f(x)=−3sec⁡(2x) f(x)=-3 \sec (2 x) , find f′(x) f^{\prime}(x) .\newlineAnswer: f′(x)= f^{\prime}(x)=
  1. Recall Secant Derivative: Recall the derivative of the secant function. The derivative of sec⁡(u)\sec(u) with respect to xx is sec⁡(u)tan⁡(u)\sec(u)\tan(u) times the derivative of uu with respect to xx (chain rule).
  2. Apply Chain Rule: Apply the chain rule to find the derivative of f(x)=−3sec⁡(2x)f(x) = -3\sec(2x). Let u=2xu = 2x, then the derivative of uu with respect to xx is dudx=2\frac{du}{dx} = 2. The derivative of f(x)f(x) with respect to xx is then f′(x)=−3⋅ddx[sec⁡(u)]⋅dudxf'(x) = -3 \cdot \frac{d}{dx}[\sec(u)] \cdot \frac{du}{dx}.
  3. Calculate Derivative: Calculate the derivative using the result from Step 11.\newlinef′(x)=−3×sec⁡(u)tan⁡(u)×2f'(x) = -3 \times \sec(u)\tan(u) \times 2\newlineSince u=2xu = 2x, we substitute back to get:\newlinef′(x)=−3×sec⁡(2x)tan⁡(2x)×2f'(x) = -3 \times \sec(2x)\tan(2x) \times 2
  4. Simplify Expression: Simplify the expression for the derivative.\newlinef′(x)=−6⋅sec⁡(2x)tan⁡(2x)f'(x) = -6 \cdot \sec(2x)\tan(2x)\newlineThis is the derivative of f(x)f(x) with respect to xx.

More problems from Transformations of absolute value functions

Question
What is the domain of this function?\newline(9,–2)(6,–10)(–3,9)(5,2)(9,–2)(6,–10)(–3,9)(5,2)\newlineChoices:\newline(A){–3,5,6,9}(B){–10,–2,2,9}(C){2,5,6,9}(D){–6,–3,5,9}(A)\{–3,5,6,9\}\newline(B)\{–10,–2,2,9\}\newline(C)\{2,5,6,9\}\newline(D)\{–6,–3,5,9\}
Get tutor helpright-arrow

Posted 1 month ago

Question
Look at this set of ordered pairs:\newline(2,14)(2, 14)\newline(10,12)(10, 12)\newline(3,−19)(3, -19)\newlineIs this relation a function?\newlineChoices:\newline[[yes]\text{[[yes]}[no]]\text{[no]]}
Get tutor helpright-arrow

Posted 1 month ago

Question
Use the following function rule to find f(11) f(11) .\newlinef(x)=−10−7x f(x) = -10 - 7x \newlinef(11)= f(11) = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the slope of the line y=−3x−25 y = -3x - \frac{2}{5} .\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
A line has a slope of 33 and passes through the point (−2,−10)(-2,-10). Write its equation in slope-intercept form.\newlineWrite your answer using integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the range of this function?\newliney = |x|\newlineChoices:\newlineall real numbers\text{all real numbers}\newline{y∣y≥0}\{y \mid y \geq 0\}\newline{y∣y≤0}\{y \mid y \leq 0\}\newline{y∣y>0}\{y \mid y > 0\}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 1 1 unit down of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the domain of this function?\newline(8,–1)(7,–11)(–4,10)(4,3)(8,–1)(7,–11)(–4,10)(4,3)\newlineChoices: \newline(A){–4,4,7,8}(A)\{–4,4,7,8\}\newline(B){–11,–1,3,10}(B)\{–11,–1,3,10\}\newline(C){3,4,7,8}(C)\{3,4,7,8\}\newline(D){–7,–4,4,8}(D)\{–7,–4,4,8\}
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the domain of this function?\newline(10, –3)(2, –9)(–5, 8)(3, 1)(10,\,–3)(2,\,–9)(–5,\,8)(3,\,1)\newlineChoices:\newline[{–5,2,3,10}][{–9, –3,1,8}][{1,2,3,10}][{–10, –5,2,3}][\{–5,2,3,10\}][\{–9,\,–3,1,8\}][\{1,2,3,10\}][\{–10,\,–5,2,3\}]
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the domain of this function?\newline(1,–4)(9,–12)(–6,11)(7,5)(1,–4)(9,–12)(–6,11)(7,5)\newlineChoices:(A){–6,1,7,9}\newline\\(A)\{–6,1,7,9\}\newline(B){–12,–4,5,11}(B)\{–12,–4,5,11\}\newline(C{5,1,7,9}(C\{5,1,7,9\}\newline(D){–9,–6,1,7}(D)\{–9,–6,1,7\}
Get tutor helpright-arrow

Posted 1 month ago

View all (45)