# Year 11 Calculus Homework mainly focusing on Quotient Rule

Hello. 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
My attempt:
(a) y' = (x-b)(1) - (x-A)(1) / (x - B)^2
y' = (2x - AB) / (x - B)^2

2. Evaluate f'(1) when
(a) f(x) = (√x) + (√2) / (√x) - (√2)
(b) f(x) = (2x-3)(√x + 1)/ x
My attempt:
(a) f'(x) = (√x-√2)(1/2√x)-(√x+√2)(1/2√x)/(√x -√2)^2
= 1/2 - √2/2√x - 1/2 + √2/2√x
= (-√2/√x)/ (√x-√2)^2
f'(1) = (-√1) / (√1-√2)^2
(-√1) = (√1-√2)^2
I'm not sure what to do from here

(b) f(x) = (2x-3)(√x + 1)/ x
u = (2x-3)(√x + 1)
v = x

f'(x) =
I don't know how to find the derivate to u. If I did I would only be able to get up to what I did in question 2. (a)

With Q1 (b) and (c) am I supposed to equate the equation to A or B, like in quadratic equations? Or is that what I am supposed to do in Question 2. I am confused by what these questions are asking. Sorry if I haven't shown as much working out as I should have.

## The Attempt at a Solution

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Dick
Homework Helper
Hello. 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
My attempt:
(a) y' = (x-b)(1) - (x-A)(1) / (x - B)^2
y' = (2x - AB) / (x - B)^2

2. Evaluate f'(1) when
(a) f(x) = (√x) + (√2) / (√x) - (√2)
(b) f(x) = (2x-3)(√x + 1)/ x
My attempt:
(a) f'(x) = (√x-√2)(1/2√x)-(√x+√2)(1/2√x)/(√x -√2)^2
= 1/2 - √2/2√x - 1/2 + √2/2√x
= (-√2/√x)/ (√x-√2)^2
f'(1) = (-√1) / (√1-√2)^2
(-√1) = (√1-√2)^2
I'm not sure what to do from here

(b) f(x) = (2x-3)(√x + 1)/ x
u = (2x-3)(√x + 1)
v = x

f'(x) =
I don't know how to find the derivate to u. If I did I would only be able to get up to what I did in question 2. (a)

With Q1 (b) and (c) am I supposed to equate the equation to A or B, like in quadratic equations? Or is that what I am supposed to do in Question 2. I am confused by what these questions are asking. Sorry if I haven't shown as much working out as I should have.

## The Attempt at a Solution

Why don't you just concentrate on 1(a) for a bit. Your simplification of the derivative is badly wrong. It's bad algebra. I don't even understand what you are doing. Then go on to the rest.

Think of exactly what the quotient rule states. How would you then apply it to the expression y = (x-a)/(x-b) ?

verty
Homework Helper
Those square roots are wrong. Practice with the sum and product rules until you know them very well, then come back to the quotient rule. I say this because once you apply the quotient rule, you'll have sums and products to simplify.