functions and differentiation

This assignment is worth 30 marks and will comprise 10% of your final grade.

The number of marks assigned to each question is listed in the right margin.

Please write your answers in pen, show full working, and staple your papers

together before submitting your assignment in class next Wednesday.

dy

1. Find the derivative E of the following functions.

(a) y= [($*1)(9€+1)l8 C

1 + tanx

b = T Z

y sinx

1 + $2

l T i

(c) y n( 962

<d> y

y _ 2 lnzv

(e) -xcosh:n+ 1

(f) y = /sin’1:v (i

1 :62

2. Consider the function = / sinx + – ln j

2 cc -1- 1

(In this course, the value of 9c in a trigonometric function such as sinx should

always be treated as a value in radians.)

(a) What is the value of the function at ct = g? (i

(b) For what values of 9c is sinx positive? (Z

(c) What is the domain of f? (i

(Hint: Try plotting the function using a computer or graphics calculator.)

(d) Find the derivative of (i

(Hint: Use logarithm laws to simplify f before differentiating it.)

(e) What is the domain of f’? (i

(f) Find the equation for the tangent and normal line to the curve at ac = (i