Solution Found!
Power rule for rational exponents Let p and q be integers
Chapter 3, Problem 48E(choose chapter or problem)
Power rule for rational exponents Let p and q be integers with \(q>0\). If \(y=x^{p / q}\), differentiate the equivalent equation \(y^{q}=x^{p}\) implicitly and show that, for \(y \neq 0\),
\(\frac{d}{d x} x^{p / q}=\frac{p}{q} x^{(p / q)-1}\).
Equation Transcription:
Text Transcription:
q>0
y=x^p/q
y^q=x^p
Y not equal to 0
d/dx x^p/q = p/q x^(p/q)-1
Questions & Answers
QUESTION:
Power rule for rational exponents Let p and q be integers with \(q>0\). If \(y=x^{p / q}\), differentiate the equivalent equation \(y^{q}=x^{p}\) implicitly and show that, for \(y \neq 0\),
\(\frac{d}{d x} x^{p / q}=\frac{p}{q} x^{(p / q)-1}\).
Equation Transcription:
Text Transcription:
q>0
y=x^p/q
y^q=x^p
Y not equal to 0
d/dx x^p/q = p/q x^(p/q)-1
ANSWER:SOLUTION:
Step 1 of 2:
In this question, let and be integers with . If , differentiate the equivalent equation implicitly and show that, for ,
