deriv of lnu
To find the derivative of ln(u), we can use the chain rule of differentiation
To find the derivative of ln(u), we can use the chain rule of differentiation.
Let’s assume that u is a differentiable function of x. Then, we can write ln(u) as ln(f(x)) = ln(u(x)).
According to the chain rule, the derivative of ln(u) with respect to x is given by:
d/dx ln(u) = (d/dx ln(u(x))) * (du(x)/dx)
Now, let’s find the derivative of ln(u(x)) and du(x)/dx separately.
The derivative of ln(u(x)) can be found using the chain rule. Let v = u(x), then:
d/dx ln(u(x)) = d/dx ln(v) = (1/v) * (dv/dx)
Here, dv/dx is the derivative of v = u(x) with respect to x.
Next, we find the derivative of u(x) with respect to x, du(x)/dx.
Combining these derivatives, we get:
d/dx ln(u) = (1/u) * (du/dx)
So, the derivative of ln(u) with respect to x is (1/u) * (du/dx).
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