Consider the functions $p$ and $q$. $p(x) = \frac{3x}{5x + 3}$ $q(x) = 8x - 1$ Calculate $r'$ if $r(x) = \frac{p(x)}{q(x)}$. $r' = $
Added by Ellen W.
Close
Step 1
p(x) = (3x)/(5x+3) To find the derivative of p(x), we can use the quotient rule: p'(x) = [(5x+3)(3) - (3x)(5)] / (5x+3)^2 p'(x) = (15x + 9 - 15x) / (5x+3)^2 p'(x) = 9 / (5x+3)^2 Show more…
Show all steps
Your feedback will help us improve your experience
Gio Maya and 79 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let $p, q,$ and $r$ be functions such that $p(z)=q(r(z))$. If $r(3)=3, q(3)=-2, r^{\prime}(3)=4,$ and $q(3)=6,$ find $p(3)$ and $p^{\prime}(3)$.
The Derivative
The Chain Rule
Consider the functions $p=\{(4,6),(2,-7),(1,0),(3,2 \pi)\}$ and $q=\left((6,4),(2,-5),\left(2, \frac{1}{3}\right),(0,9)\right) .$Find the function values. $$q(0)$$
Linear Equations in Two Variables and Functions
Introduction to Functions
Consider the functions $p=\left\{\left(\frac{1}{2}, 6\right),(2,-7),(1,0),(3,2 \pi)\right\}$ and $q=\left\{(6,4),(2,-5),\left(\frac{3}{4}, \frac{1}{5}\right),(0,9)\right\} .$ Find the function values. $$q(0)$$
Relations and Functions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD