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 the following table of values, find h^(')(2) if {:[h(x)=(4)/(x^(3))+(f(x))/(g(x))". "],[{:[x,f(x),f^(')(x),g(x),g^(')(x)],[2,3,-3,3,1]:}]:}

Given the following table of values, find h′(2) h^{\prime}(2) if\newlineh(x)=4x3+f(x)g(x). xf(x)f′(x)g(x)g′(x)23−331 \begin{array}{l} h(x)=\frac{4}{x^{3}}+\frac{f(x)}{g(x)} \text {. } \\ \begin{array}{rrrrr} x & f(x) & f^{\prime}(x) & g(x) & g^{\prime}(x) \\ \hline 2 & 3 & -3 & 3 & 1 \end{array} \\ \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find higher derivatives of rational and radical functionsright chevron icon

Full solution

Q. Given the following table of values, find h′(2) h^{\prime}(2) if\newlineh(x)=4x3+f(x)g(x). xf(x)f′(x)g(x)g′(x)23−331 \begin{array}{l} h(x)=\frac{4}{x^{3}}+\frac{f(x)}{g(x)} \text {. } \\ \begin{array}{rrrrr} x & f(x) & f^{\prime}(x) & g(x) & g^{\prime}(x) \\ \hline 2 & 3 & -3 & 3 & 1 \end{array} \\ \end{array}
  1. Identify function and values: Identify the function and values needed:\newlineh(x)=4x3+f(x)g(x)h(x) = \frac{4}{x^3} + \frac{f(x)}{g(x)}\newlineFrom the table, at x=2x = 2, f(2)=3f(2) = 3, f′(2)=−3f'(2) = -3, g(2)=3g(2) = 3, g′(2)=1g'(2) = 1.
  2. Apply quotient rule: Apply the quotient rule to find the derivative of the second term (f(x)/g(x))(f(x)/g(x)):(f(x)/g(x))′=(f′(x)g(x)−f(x)g′(x))/g(x)2(f(x)/g(x))' = (f'(x)g(x) - f(x)g'(x)) / g(x)^2Plugging in the values: (f′(2)g(2)−f(2)g′(2))/g(2)2=(−3⋅3−3⋅1)/32=(−9−3)/9=−12/9=−4/3(f'(2)g(2) - f(2)g'(2)) / g(2)^2 = (-3\cdot3 - 3\cdot1) / 3^2 = (-9 - 3) / 9 = -12 / 9 = -4/3.

More problems from Find higher derivatives of rational and radical functions

Question
f′(x)=12ex and f(4)=−16+12e4.f(0)= \begin{array}{l}f^{\prime}(x)=12 e^{x} \text { and } f(4)=-16+12 e^{4} . \\ f(0)=\end{array}
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for nn.83=12nn=□\begin{array}{l}\frac{8}{3}=\frac{12}{n} \\ n=\square\end{array}
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the equation. b6=3b=□\begin{align*} \frac{b}{6} &= 3 \\ b &= \Box \end{align*}
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the equation. \begin{align*} \frac{b}{6} &= 3, \ b &= \Box \end{align*}
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for nn.125=n8\frac{12}{5}=\frac{n}{8} \newline n=□n = \Box
Get tutor helpright-arrow

Posted 2 months ago

Question
The second derivative of the function f f is defined by f′′(x)=x2−5cos⁡(2x) f^{\prime \prime}(x)=x^{2}-5 \cos (2 x) for −2.5<x<3.5 -2.5<x<3.5 . Find the x x -values, if any, in the given domain where the function f f has an inflection point. You may use a calculator and round all values to 33 decimal places.\newlineAnswer: x= x=
Get tutor helpright-arrow

Posted 2 months ago

Question
f′(x)=12ex and f(4)=−16+12e4.f(0)= \begin{array}{l}f^{\prime}(x)=12 e^{x} \text { and } f(4)=-16+12 e^{4} . \\ f(0)=\end{array}
Get tutor helpright-arrow

Posted 2 months ago

Question
x2−6x+11=yx=y+1 \begin{array}{c}x^{2}-6 x+11=y \\ x=y+1\end{array}
Get tutor helpright-arrow

Posted 2 months ago

Question
=x2+4=(g+h)(x) \begin{array}{l} =x^{2}+4 \\ =(g+h)(x) \end{array} \newline99.\newlineh(x)=x2+xg(x)=3x+5 Find (h⋅g)(x) \begin{array}{l} h(x)=x^{2}+x \\ g(x)=3 x+5 \\ \text { Find }(h \cdot g)(x) \end{array}
Get tutor helpright-arrow

Posted 2 months ago

Question
Factor completely:\newline8c3+27m6 8 c^{3}+27 m^{6} \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

View all (33)