In this case, you need to apply the chain rule. Note that the derivative of ln N = 1/N. In that case we get:
f(x) = ln(1 - x)
∴ f'(x) = 1/(1 - x) × -1
∴ f'(x) = -1/(1 - x)
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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.
If the function is (ln x)2, then the chain rules gives us the derivative 2ln(x)/x, with the x in the denominator. If the function is ln (x2), then the chain rule gives us the derivative 2/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
ln(3) is a constant. If graphed, it would be a horizontal line. Its derivative is zero.
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x