I just need my work checked, derivatives

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    Derivatives Work
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Homework Help Overview

The discussion revolves around finding derivatives of various functions, specifically involving logarithmic and implicit differentiation. The original poster presents three derivative problems, including a logarithmic function and an implicit function.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to solve derivative problems using standard differentiation techniques, including the product rule and implicit differentiation. Some participants question the correctness of the original poster's solutions, while others suggest alternative approaches to the first problem, specifically rewriting the logarithmic expression.

Discussion Status

The discussion includes attempts to verify the correctness of the original poster's answers, with some participants providing feedback and alternative methods. There is an acknowledgment of the learning process involved in differentiation, and while some guidance has been offered, there is no explicit consensus on the correctness of the answers.

Contextual Notes

Participants note the context of learning derivatives for the first time, which may influence the nature of the questions and responses. The original poster's request for verification indicates a desire for confirmation rather than a complete solution.

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Homework Statement


I just need to find the derivatives of the following:
[a] y=ln(x^4 sin^2 x)
f(x) = x^2 lnx, also find f'(1)
[c] x^y = y^x

Homework Equations


See above


The Attempt at a Solution


[a] y' = [(4x^3)(sin^2x) + (x^4)(2sinxcosx)]/(x^4sin^2x) = (4sinx + 2xcosx)/(xsinx)

f(x)' = (2x)(lnx) + (x^2)(1/x) = 2xlnx + x
f'(1) = 2(1)ln(1) + 1 = 2(0) + 1 = 1

[c] ln(x^y) = ln(y^x)
ylnx = xlny
d/dx ( ylnx) = d/dx (xlny)
(1)(y')(lnx) + (y)(1/x) = (1)(lny) + (x)(1/y)(y')
lnxy' + y/x = lny + xy'/y
lnxy' - xy'/y = lny = y/x
y'(lnx - x/y) = lny - y/x
y' = (lny - y/x)/(lnx - x/y)
 
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Ridiculously boring. Who gives you those exercises?
 
Werg22 said:
Ridiculously boring. Who gives you those exercises?

Professors who KNOW that their students are doing derivatives for the first time.
 
LOL...are my answers correct?
 
JasonRox said:
Professors who KNOW that their students are doing derivatives for the first time.
Good point; we all had to learn differentiation at some point. There's no need for such a pompous reply.
FlipStyle1308 said:
LOL...are my answers correct?
Yes, presuming that the last question is asking for the derivative wrt x.
 
Great, thank you!
 
By the way, for [a] y=ln(x^4 sin^2 x)
I would write y= 4 ln x+ 2 ln sin x and get
[tex]y'= \frac{4}{x}+ 2\frac{cos x}{sin x}[/tex]
Can you show that is the same as your answer?
 

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