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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
What is the Second derivative of lnx?
-1/x2
How do you solve for x when the natural log of the square root of x equals the square root of the natural log of x?
ln(√x)=√(lnx) because √x = x^(1/2), ln(x^(1/2))=√(lnx) using a logarithmic property, we can say that .5(lnx)=√(lnx) now, pretend that lnx=y .5y=√y square both sides .25y^2=y subtract y from both sides .25y^2 -y=0 factor y(.25y - 1)=0 so either y=0 or .25y -1 =0 If .25y -1=0, then y=4 so lnx=0 or lnx=4 lnx cannot equal zero because lnx=0 means e^x=0 and that is impossible. Now, we are left with lnx=4 Isolate x by making both sides of the equation powers of e: e^(lnx)=e^4 x=e^4, which is approximately 54.6 Lastly, check this answer by plugging e^4 back into the original equation: ln(√(e^4))=√(ln(e^4)) ln(e^2)=√(4(lne)) 2lne=2√1 2(1)=2 2=2 There you go!
What is the derivative of lnx?
Derivative of lnx= (1/x)*(derivative of x) example: Find derivative of ln2x d(ln2x)/dx = (1/2x)*d(2x)/dx = (1/2x)*2===>1/x When the problem is like ln2x^2 or ln-square root of x...., the answer won't come out in form of 1/x.
How do you evaluate definite integrals?
In order to evaluate a definite integral first find the indefinite integral. Then subtract the integral evaluated at the bottom number (usually the left endpoint) from the integral evaluated at the top number (usually the right endpoint). For example, if I wanted the integral of x from 1 to 2 (written with 1 on the bottom and 2 on the top) I would first evaluate the integral: the integral of x is (x^2)/2 Then I would subtract the integral evaluated at 1 from the integral evaluated at 2: (2^2)/2-(1^2)/2 = 2-1/2 =3/2.
Integral of xlnxdx?
integration by parts. Let u=lnx, dv=xdx-->du=(1/x)dx, v=.5x^2. Integral of (xlnxdx)=lnx*.5x^2-integral of .5x^2(1/x)dx=lnx*.5x^2-integral of .5xdx=lnx*.5x^2-(1/6)x^3. That's it.
What is the integral of lnx?
xln(x)-x
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
What is the integral of x.lnx?
Do you want ∫x lnx dx? Let's call that I, which we now seek to find. The solution is I = ½ x2 lnx - ¼ x2; here is how we can find it: Let z = lnx. Then, x = ez, dx = ez dz, and dI = x lnx dx. Then, dI = (ez)(z)(ez dz) = ze2z dz = ¼ (2z e2z d(2z)). Thus, 4dI = wew dw, where we let w = 2z = 2 lnx. Now, d(wew) = ew dw + w d(ew) = ew dw + wew dw = ew dw + 4dI; hence, 4dI = d(wew) - ewdw = d(wew) - d(ew)­ = d((w - 1)ew). Therefore, 4I = (w - 1)ew = (2 lnx - 1)x2 = 2x2 lnx - x2; and I = ½ x2 lnx - ¼ x2, which is the answer we sought. Checking, we differentiate back, to confirm that I' = x lnx: I = ¼ x2(2 lnx - 1), whence, 4I' = (x2(2 lnx - 1))' = 2x(2 lnx - 1) + x2 (2/x) = 2x(2 lnx - 1) + 2x = 2x(2 lnx) = 4x lnx; thus, I' = x lnx, re-assuring us that we have integrated correctly.
What is the derivative of 1-lnx divided by 2x?
-1
Simplify e to the 1 plus Inx power?
e1 + (lnx) = e1 * e(lnx) = e * x = ex
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]
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 lnx raised to 4?
ln(x4)?d/dx(ln(u))=1/u*d/dx(u)d/dx(ln(x4))=[1/x4]*d/dx(x4)-The derivative of x4 is:d/dx(x4)=4x4-1d/dx(x4)=4x3d/dx(ln(x4))=[1/x4]*(4x3)d/dx(ln(x4))=4x3/x4d/dx(ln(x4))=4/x(lnx)4?Chain rule: d/dx(ux)=x(u)x-1*d/dx(u)d/dx(lnx)4=4(lnx)4-1*d/dx(lnx)d/dx(lnx)4=4(lnx)3*d/dx(lnx)-The derivative of lnx is:d/dx(ln(u))=1/u*d/dx(u)d/dx(lnx)=1/x*d/dx(x)d/dx(lnx)=1/x*(1)d/dx(lnx)=1/xd/dx(lnx)4=4(lnx)3*(1/x)d/dx(lnx)4=4(lnx)3/x
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
How do you rearrange u equals 1 plus lnx to get x equals?
If: u = 1+lnx Then: x = (u-1)/(ln)
Derivative of lnx?
1/X
