Calc

a) y =ln(x-1) find dy/dx=?
b) y=3 ln x - ln (1/x) where x >0, dy/dx= ?

My teacher says the answers are a) (2x)/(x^2-1) and b) 4/x
I am not sure how you find the derivative when they involve ln. Could you please explain to me how to get these answers? I have a quiz on them soon so I just want to clearify how you would solve them. Thanks.

<<I am not sure how you find the derivative when they involve ln.>>

The derivative of ln x is 1/x. Use the "function of a function" rule when the log is of a function of x. For example:
y = ln (x-1)
Let u(x) = x-1
dy/dx = d (ln u)/du * du/dx = 1/u
= 1/(x-1)
You teacher is wrong on that one.

(2x)/(x^2-1)is the derivative of
ln (x^2 -1)
Perhaps you copied the problem wrong.

If y = 3 ln x - ln (1/x)
y = 3 ln x + ln x = 4 ln x
dy/dx = 4/x

asked by Jamie

Respond to this Question

First Name

Your Response

Similar Questions

  1. calc

    derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2 - 1/(2x^2) you are correct I don't think they are looking for the square of
  2. Calc (Derivatives)

    I understand finding the derivative and there is a simpler way of doing so, however, can someone show you derive at these answers by the DEF'N of Derivatives? Much appreciated! Question 1: Find, from the definition, the
  3. Calc I

    if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t-1)^-1/2 * 4t^3 and i'm trying to figure out if i need the product rule again to find the second derivative -1t^3(4t-1)^-3/2 * 4t^3 The answer if -4/27 and I'm
  4. Derivative Calculus

    I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4 - 8/9x^9/8 + x^2 - 9x + 1 Answer: f’(x)= 15/4x^1/4 - x ^1/8 + 2x -9 2) Let f(x)= 7x^3 - 9x. Find f’(5) Answer: f’(x)=21x^2-9 f’(5)=516 3) Find the given
  5. CALC 1

    Suppose that h is a function with h'(x) = xe^x. Find all intervals where the function h is concave up. Now, I understand that concavity is determined by the second derivative, so what my question here is, is it just taking the
  6. Calc I

    I'm a little confused about this one, it seems different from the rest of our homework! Could someone give me some hints? Thank you! Find the first and second derivative of the function. Check to see that your answers are
  7. Calc-Derivative

    Find the derivative of x^(1/x). Can someone show me steps for this problem...I go round in circles
  8. Calc.

    find the derivative of 3x^4-5x+3/x^4+1 i know that the derivative of the numeratoor would be 12x^3-5 but i'm not sure if its right since it has a denominator i Know i need to do something to it but not sure if to simplify.
  9. Calc Help

    Find two functions that this could be the derivative of: y'=4x+7 Remember the derivative of any constant is zero. take its antiderivative i suppose... y= 2x^2 + 7x + any number
  10. Calc

    1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)<0 if x<4

More Similar Questions