How do I find the derivative of #ln(x)^2#?

Answer 1

Emily Ammerman

# dy/dx=2/x#.

#y=lnx^2=2lnx#

#:. dy/dx=d/dx(2lnx)=2d/dx(lnx)=2*1/x=2/x#.

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Answer 2

Samantha Adkison

To find the derivative of ln(x)^2, you can use the chain rule. Start by recognizing that ln(x)^2 can be rewritten as (ln(x))^2. Then, differentiate (ln(x))^2 with respect to x using the chain rule, which states that the derivative of f(g(x)) with respect to x is f'(g(x)) * g'(x). Here's the step-by-step process:

Let u = ln(x).
Rewrite ln(x)^2 as u^2.
Differentiate u^2 with respect to u: d(u^2)/du = 2u.
Differentiate ln(x) with respect to x: d(ln(x))/dx = 1/x (using the derivative of ln(x) = 1/x).
Apply the chain rule: d(ln(x)^2)/dx = d(ln(x)^2)/du * du/dx = 2u * (1/x).
Substitute u = ln(x): 2(ln(x)) * (1/x).
Simplify: 2ln(x)/x.

So, the derivative of ln(x)^2 with respect to x is 2ln(x)/x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.