# How do you find the first and second derivative of #lnx^2 #?

Using the chain rule we get:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the first and second derivatives of ( \ln(x^2) ), you can use the chain rule and the power rule.

First derivative: [ \frac{d}{dx}(\ln(x^2)) = \frac{1}{x^2} \cdot 2x = \frac{2}{x} ]

Second derivative: [ \frac{d^2}{dx^2}(\ln(x^2)) = \frac{d}{dx}\left(\frac{2}{x}\right) = -\frac{2}{x^2} ]

So, the first derivative is ( \frac{2}{x} ) and the second derivative is ( -\frac{2}{x^2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

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.

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.

- How do you find the x and y coordinates of all inflection points #f(x) = x^4 - 12x^2#?
- What are the points of inflection of #f(x)=1/(1+x^2)#?
- Is #f(x)=-2x^3-2x^2+8x-1# concave or convex at #x=3#?
- How do you compare either points (0,0) and (-1,-1) to see if it is max min or point of inflection for #y= 36x^2 +24x^2#?
- How do you determine whether the function #f(x)= 4/(x^2+1)# is concave up or concave down and its intervals?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7