The Power Rule can be proved using implicit differentiation for the case where n is a rational number, n p q, and y f (x) x n is assumed beforehand to be a differentiable function If y x p q , then yq x p Use implicit differentiation to show that y' Lx0 w L p q)

Question: The Power Rule can be proved using implicit differentiation for the case where n is a rational number, n = p/q, and y = f

The Power Rule can be proved using implicit differentiation for the case where n is a rational number, n = p/q, and y = f (x) = xⁿ is assumed beforehand to be a differentiable function. If y = x^p/q, then yq = x p. Use implicit differentiation to show that

y' = Lx0/w-L p/q)

Step by Step Solution

★★★★★

3.39 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Y9 XP qy91 p... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Find the derivative of f(x) with the chain rule. The equation for the top half of a circle is f(x) = 1 - x2. In addition to using implicit differentiation (Example 2.9.10), we can find the slope of...

(a) Explain how implicit differentiation works. (b) Explain how logarithmic differentiation works.

The number of grams of radium, y, that will remain after t years if 100 grams existed originally can be found by using the equation Use implicit differentiation to find the rate of change of y with...

Need an example of this to see how this works. This week, we're seeing how the derivatives of inverse functions y =f (x ) can be found by looking at f(y) = 1 , and using implicit differentiation....

X Standard form - Ximera X + -> C ximera.osu.edu/mooculus/calculus1TextbookBySection/implicitDifferentiation/implicitDifferentiation/breakGround H Men Custom Suits... BASEXX... O BERHAS 20... b Big...

In Algebra 2, you learned several different methods for solving quadratic equations. For example, you could try factoring, completing the square, or just use the quadratic formula since it ALWAYS...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Read the article, "John D.R. Leonard, Plaintiff, -against- PepsiCo, Inc., Defendant," found on the website provided in the Reading & Study folder. Watch the presentations (also found in the Reading &...

Specification and Verification II Consider the following Verilog phrases: initial r = 0; always @(posedge clk) r = a + r; Write down a formula in logic that relates clk, a and r at a level of...

Recall that we proved that (a) = na-1 for all positive integers n (the so-called "power rule"). (a) Derive the power rule in the case where n > 0 is rational, i.e. n = p/q, where p and q are integers...

Carver Inc. purchased a building and the land on which the building is situated for a total cost of $700,000 cash. The land was appraised at $320,000 and the building at $480,000. Required a....

6. Consider a system of angular momentum l = 1. A basis of its state space is formed by the three eigenvectors of L2: |+ 1), |0), | 1), whose eigenvalues are, respectively, +h, 0, and -h, and which...

Four members of a group of 10 people are to be selected to a team. How many ways are there to select these four members?

Based on Exhibit 1 and assuming interest rates remain unchanged, which bond will have the highest hedged return? A . UK 10-year. B . Japan 10-year. C . Germany 10-year.

Verify that the function satisfies the three hypotheses of Rolles Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolles Theorem. f(x) x 3 - 2x 2 - 4x + 2, [22,...

Use the graph to state the absolute and local maximum and minimum values of the function. y=g(x) 1 1

Prove the identity. tanh(x + y) = tanh x + tanh/1 + tanh x tanh y

Barton Industries estimates its cost of common equity by using three approaches: the CAPM, the bond-yield-plus-risk-premium approach, and the DCF model. Barton expects next year's annual dividend,...

Amarindo, Inc. (AMR), is a newly public firm with 10.0 million shares outstanding. You are doing a valuation analysis of AMR. You estimate its free cash flow in the coming year to be $14.86 million,...

How is this done? Markus Co. is a manufacturing firm. Markus Co.'s current value of operations, including debt and equity, is estimated to be $10 million. Markus Co. has $4 million face-value zero...