- #1
josh_123
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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
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
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