Calculus (topic 5)

Question 1

The limit of a function

Answer 1

Is the value a function (of x) approaches as x approaches a particular value from either side

Question 2

The derivative of a function

Answer 2

Is a function that relates the gradient to the value of x. Also called the gradient function

Question 3

Derivative of a constant term

Answer 3

Always 0

Question 4

Derivative for the function y = f(x)

Answer 4

dy/dx = f’(x)

Question 5

To differentiate a/x^n, write it in what form?

Answer 5

ax^-n

Question 6

To differentiate a^m * squareroot of x^n, write it in what form?

Answer 6

ax^n/m

Question 7

Differentiation

Answer 7

The process used to find the derivative function

Question 8

Derivative of y = sin(2x) (derivative of sin x)

Answer 8

y’ = 2cos(2x)

Question 9

Derivative of y = 3cos(2x - 1) (derivative of cos x)

Answer 9

y’ = -6sin(2x - 1)

Question 10

Derivative of f(x) = e^2x and y = e^(x^2) - 3 (derivative of e^x)

Answer 10

f’(x) = 2e^2x and y’ = 2x * e^(x^2) - 3

Question 11

Derivative of y = ln (2x + 1) (derivative of ln x)

Answer 11

y’ = 2/(2x + 1)

Question 12

Derivative of y = (2x + 1)^5 (chain rule)

Answer 12

y’ = 5(2x + 1)^4 * 2(derivative of equation)
y’ = 10(2x + 1)^4

Question 13

Derivative of y = (2x + 1)(x - 2) (product rule)

Answer 13

u = (2x + 1), v = (x - 2)
u’ = 2, v’ = 1
y’ = uv’ + vu’

y’ = 1(2x + 1) + 2(x - 2)
y’ = 2x + 1 + 2x - 4
y’ = 4x - 3

Question 14

Derivative of y = 3x - 2 / x + 5 (quotient rule)

Answer 14

u = 3x - 2, v = x + 5
u’ = 3, v’ = 1
y’ = (vu’ - uv’) / v^2

y’ = 3(x + 5) - 1(3x - 2) / (x + 5)^2
y’ = (3x + 15 - 3x + 2) / (x + 5)^2
y’ = 17 / (x + 5)^2