Chapter 12 - Differentiation

Question 1

What is the gradient of a curve at a given point defined as?

Answer 1

The gradient of the tangent to the curve at that point.

Question 2

What 2 ways are there to write the gradient function or derivative of a curve?

Answer 2

f’(x)

Or

dy
—
dx

Question 3

What is the gradient function of a curve (first principle)?

Answer 3

f(x + h) - f(x)
F’(x) = lim ——————
h -> 0 h

Question 4

If f(x) = x^n or y = x^n then what does f’(x) or
dy
—
dx

Make?

Answer 4

They both make

nx^n-1

Question 5

If f(x) = ax^n or y = ax^n then what does f’(x) or
dy
—
dx

Make?

Answer 5

They both make

anx^n-1

Question 6

For the quadratic curve with the equation

ax^2 + bx + c

what is the derivative of that curve?

Answer 6

dy
— = 2ax + b
dx

Question 7

If y = f(x) +- g(x) then what is he derivative?

Answer 7

dy
— = f’(x) +- g’(x)
dx