derv (ln u)
To find the derivative of ln(u), we can use the chain rule
To find the derivative of ln(u), we can use the chain rule. The chain rule states that if we have a composition of functions, such as ln(u), where u is a function of some variable, then the derivative is given by the derivative of the outer function multiplied by the derivative of the inner function.
Let’s differentiate ln(u) step by step:
Step 1: Identify the inner function.
In this case, the inner function is u.
Step 2: Differentiate the inner function.
The derivative of u with respect to the variable it depends on will give us du/dx, where x is the variable.
Step 3: Differentiate the outer function.
The derivative of ln(u) with respect to u is 1/u.
Step 4: Combine the derivatives using the chain rule.
Applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function:
d/dx [ln(u)] = (1/u) * du/dx
And that is the derivative of ln(u) using the chain rule.
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