Derivative of ln x
1/x
The derivative of ln x is:
d/dx ln x = 1/x
You can use the logarithmic differentiation rule to derive this.
To apply logarithmic differentiation, we start by taking the natural logarithm of both sides of the function we want to differentiate. So, we have:
ln y = ln x
Next, we need to differentiate both sides with respect to x. Remembering that ln a is equal to 1/a, we get:
d/dx ln y = d/dx ln x
1/y * dy/dx = 1/x
Now, we can solve for dy/dx to get the derivative of ln x:
dy/dx = y/x
We know that y = ln x, so we can substitute this back in:
dy/dx = ln x/x
Recall that ln x is equal to log base e of x. Therefore, we can write:
d/dx ln x = 1/x
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