(adsbygoogle = window.adsbygoogle || []).push({}); I need help in finding dy/dx or the derivative of these function:

1. y=sin^2(lnx)

so d/dx[sin^2(lnx)] I tried following this model of sin^x=(sinx)^2 so d/dx[(sinlnx)^2)]. Then use the chain rule of dy/dx= f'g(g') which is 2(sinlnx)(cos1/x) but I don't think that is right so can you please tell me another way to do it?thank you!

2. y=x[log2(x^2-2x)]^3

d/dx[xlog2(x^2-2x)]^3=3log2(x^2-2x)^2---> Again I don't think this is right so please direct me to the right one.

3. y=exp(sqrt(1+5x^3)). This one I don't even know how to begin. Exponent of what?

4. y=ln(cose^x) using the rule of d/dx[lnu]=1/u x (du/dx) I get dy/dx=(1/cose^x)(-sin(e^x)(e^x)

dy/dx=(1/cose^x)(-e^xsine^x)

dy/dx=(-e^xsine^x)/(cose^x)---> (tane^x)(-e^x)=-e^xtane^x~Please tell me if I did anything wrong

5. Finding the derivative by using implict differentation

y=ln(xtany). Please help me get started

6. Finding the derivative by using logarithmic differentation:

y=5root(x-1/x+1) or (x-1/x+1)^1/5

lny=ln(x-1/x+1)^(1/5)=(1/5)ln(x-1/x+1)

d/dx[(1/5)ln(x-1/x+1)]=(1/5)(x-1/x+1)(2/(x+1)^2+0(ln(x^2+1)

so dy/dx=y[(2x+2)/(5x-5)(x+1)^2]

=5root(x-1/x+1)[2x+2/(5x-5)(x+1)^2]

Is this right?

~Thank you in advance =D

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding derivative of log and lnx. Please help! Need help before test!

**Physics Forums | Science Articles, Homework Help, Discussion**