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If you mean: y =(lnx)3

then:

dy/dx = [3(lnx)2]/x

ddy/dx = [(6lnx / x) - 3(lnx)2] / x2

If you mean: y = ln(x3)

Then:

dy/dx = 3x2/x3 = 3/x = 3x-1

ddy/dx = -3x-2 = -3/x2

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Q: What is the derivative and second derivative of lnx to the third power?
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Related questions

What is the Second derivative of lnx?

-1/x2


What is the Derivative of x to the power of x?

The solution to this is: (xx)'= (elnx to the power of x)'= (exlnx)'= (xlnx)'*exlnx= [x(1/x) + 1(lnx)]*exlnx = (lnx+1)*exlnx= (lnx+1)*xx


What is the derivative of 1 lnx?

The derivative of 1/lnx, can be found easily using either the chain rule or the quotient rule. It is -1/[x*(lnx)2]


Derivative of lnx?

1/X


What is the third derivative of lnx?

Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.


What is the derivative of 1-lnx divided by 2x?

-1


What is the derivative of lnx raised to lnx?

start by setting y=lnx^lnx take ln of both sides lny=lnx(ln(lnx)) differentiate dy/dx(1/y)=(1+ln(lnx))/x dy/dx=y(1+ln(lnx))/x we know that y=lnx^lnx so we can just substatute back in dy/dx=(lnx^lnx)*(1+ln(lnx))/x


X the power of x Derivative?

I get x*x^x-1 + lnx*x^x = x^x + x^xlnx = x^x * (1+lnx) Here, ^ is power; * = times; ln = natural logratithm ( base e)


What is the derivative of lnx squared?

I do not see why the chain rule would not work here. d/dx (inx)^2 = 2(lnx) * 1/x = 2(lnx)/x


What is the second derivative of x2 ln x?

First one: f'(x) = 2x*lnx + x^2*(1/x) = 2x*lnx + x = x*(2*lnx + 1) Second derivate: f"(x) = D [x*(2*lnx + 1)] = 1*(2*lnx + 1) + x*(2/x) = 2*lnx+1+2 = 2*lnx + 3 So, there is a minimum in this graph on point (1/e^(1/2)), -1/(2e)) = MIN(x, y) Van Sanden David Belgium


What is the derivative of natural log?

d/dx lnx=1/x


What is the anti derivative of lnx?

x (ln x + 1) + Constant