0
ln(1)/[1-x]?
d/dx(u/v)=(v*du/dx-u*dv/dx)/(v2)
d/dx(ln(1)/[1-x])=[(1-x)*d/dx(ln1)-ln1*d/dx(1-x)]/[(1-x)2]
-The derivative of ln1 is:
d/dx(lnu)=(1/u)*d/dx(u)
d/dx(ln1)=(1/1)*d/dx(1)
d/dx(ln1)=(1)*d/dx(1)
d/dx(ln1)=d/dx(1)
-The derivative of 1-x is:
d/dx(u-v)=du/dx-dv/dx
d/dx(1-x)=d/dx(1)-d/dx(x)
d/dx(ln(1)/[1-x])=[(1-x)*d/dx(1)-ln1*(d/dx(1)-d/dx(x))]/[(1-x)2]
-The derivative of 1 is 0 because it is a constant.
-The derivative of x is:
d/dx(xn)=nxn-1
d/dx(x)=1*x1-1
d/dx(x)=1*x0
d/dx(x)=1*(1)
d/dx(x)=1
d/dx(ln(1)/[1-x])=[(1-x)*(0)-ln1*(0-1)]/[(1-x)2]
d/dx(ln(1)/[1-x])=[-ln1*(-1)]/[(1-x)2]
d/dx(ln(1)/[1-x])=[ln1]/[(1-x)2]
But you see, ln1 is equal to 0:
d/dx(ln(1)/[1-x])=[0]/[(1-x)2]
d/dx(ln(1)/[1-x])=0
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What is the Derivative of 500 ln x plus 1?
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x
What is the derivative of ln 1- x?
The derivative of ln x is 1/x. Replacing the expression, that gives you 1 / (1-x). By the chain rule, this must then be multiplied by the derivative of (1-x), which is -1. So, the final result is -1 / (1-x).
What is the anti-derivative of x2 1x?
The antiderivative of x2 + x is 1/3x3 + 1/2x2 + C.
Is there a function where the first derivative goes to infinity for x going to 0 and where the first derivative equals 0 when x is 1?
Yes, the function ln(x) where ln is the logarithm to base e.Yes, the function ln(x) where ln is the logarithm to base e.Yes, the function ln(x) where ln is the logarithm to base e.Yes, the function ln(x) where ln is the logarithm to base e.
If y equals log x what is dy over dx?
Assuming that is the natural logarithm (logarithm to base e), the derivative of ln x is 1/x. For other bases, the derivative of logax = 1 / (x ln a), where ln a is the natural logarithm of a. Natural logarithms are based on the number e, which is approximately 2.718.
What is the third derivative of lnx?
The third derivative of ln(x) is -2/(x^3). To find the third derivative, we first find the first derivative of ln(x), which is 1/x. The second derivative is -1/x^2, and the third derivative is 2/(x^3) after applying the power rule for differentiation.
What is the derivative of Ln10?
The derivative of ln(10) is 1/10. This is because the derivative of the natural logarithm function ln(x) is 1/x. Therefore, when differentiating ln(10), the derivative is 1/10.
What is the derivative of lnlnx?
1/xlnx Use the chain rule: ln(ln(x)) The derivative of the outside is1/ln(x) times the derivative of the inside. 1/[x*ln(x)]
What is the Derivative of 500 ln x plus 1?
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x
Derivative of log?
The derivative of a log is as follows: 1 divided by xlnb Where x is the number beside the log Where b is the base of the log and ln is just the natural log.
What is the derivative of ln 1?
It is equal to 0
What is 1x divided by 1?
1
What is the derivative of e the the power ln x?
y = e^ln x using the fact that e to the ln x is just x, and the derivative of x is 1: y = x y' = 1
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
What is the derivative of ln1 divided by x?
Given y=ln(1/x) y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function. So it's 1/(1/x) [the derivative of the outside function, natural log] times -x-2=1/x2 [the derivative of the inside of the function, 1/x] This all simplifies to 1/x So the derivative of ln(1/x) is 1/x
What is the derivitive of ln10x?
The derivative of ln(x) is 1/x. Therefore, by Chain Rule, we get:[ln(10x)]' = 1/10x * 10 = 1/xUsing this method, you can also infer that the derivative of ln(Ax) where A is any constant equals 1/x.
What is the derivative of ln 1- x?
The derivative of ln x is 1/x. Replacing the expression, that gives you 1 / (1-x). By the chain rule, this must then be multiplied by the derivative of (1-x), which is -1. So, the final result is -1 / (1-x).
