Please help solve these calculus questions

[PeiPei]

I am studying differential calculus and I need help on what these questions are asking and how to solve them. I have attempted some of the question but I need clarification. This week is mainly focused on learning the Quotient Rule. Please help me

1. (a) Differentiate y = (x - A)/(x - B)
(b) Show that for A>B, all tangents have a positive gradient, and for A<B all tangent have a negative gradient
(c) What happens when A = B

2. Evaluate f'(1) when
(a) f(x) = (square root of x) + (square root of 2) / (square root of x) - (square root of 2)
(b) f(x) = (2x-3)(square root of x + 1)/ x

3.
(a) Suppose y = u/x', where u is a function of x, show that y + x dy/dx + du/dx
(b) Suppose y = x/u', where u is a function of x, show that y du/dx + u dy/dx = 1

Thank you so much for reading

 

[lookagain]

I am studying differential calculus and I need help on what these questions are asking and how to solve them. I have attempted some of the question but I need clarification. This week is mainly focused on learning the Quotient Rule. Please help me

1. (a) Differentiate y = (x - A)/(x - B)
(b) Show that for A>B, all tangents have a positive gradient, and for A<B all tangent have a negative gradient
(c) What happens when A = B

2. Evaluate f'(1) when
(a) f(x) = (square root of x) + (square root of 2) / (square root of x) - (square root of 2)
(b) f(x) = (2x-3)(square root of x + 1)/ x

3.
(a) Suppose y = u/x', where u is a function of x, show that y + x dy/dx + du/dx
(b) Suppose y = x/u', where u is a function of x, show that y du/dx + u dy/dx = 1

Thank you so much for reading

PeiPei, no, don't post a bunch of problems. Post your work here on one
problem so that we may know where you are stuck. Please read the rules before posting here:

http://www.freemathhelp.com/forum/threads/41538-Read-Before-Posting

 

[DrPhil]

I am studying differential calculus and I need help on what these questions are asking and how to solve them. I have attempted some of the question but I need clarification. This week is mainly focused on learning the Quotient Rule. Please help me

1. (a) Differentiate y = (x - A)/(x - B)
(b) Show that for A>B, all tangents have a positive gradient, and for A<B all tangent have a negative gradient
(c) What happens when A = B

2. Evaluate f'(1) when
(a) f(x) = (square root of x) + (square root of 2) / (square root of x) - (square root of 2)
(b) f(x) = (2x-3)(square root of x + 1)/ x

3.
(a) Suppose y = u/x', where u is a function of x, show that y + x dy/dx + du/dx
(b) Suppose y = x/u', where u is a function of x, show that y du/dx + u dy/dx = 1

Thank you so much for reading

In each case, the first step is to differentiate by using the quotient rule.

For number 1, you have to look at the sign of the derivative, which is the slope.

For 2, when typing inline it would look better as
a) f(x) = [sqrt(x) + sqrt(2)]/[sqrt(x) - sqrt(2)]
b) f(x) = (2x - 3)(sqrt(x + 1)/x
Note the use of extra brackets to identify numerator and denominator.
First differentiate, then evaluate at x=1

At the very least, we need to see your derivatives. We can't give guidance if we don't know where you are stuck.