Differential Calculus

Derivatives

100

What is the derivative of y = 3x² - 4

dy/dx = 6x

200

What is the first derivative of y = sqrt(x)

y' = 1/ (2sqrt(x) )

300

Differentiate y = 6x⁴ - x²/2 - 10

y' = 24x³ - x

400

Find the rate of change of the function f(x) =3/(x^1/3)

f'(x)=-1/x^4/3

Applications

100

Find the slope of the tangent line of y = 5x² - 4x at x = 1.

6

200

What is the equation of the tangent line to y = 2x³ - 6 at (-1,-8)

y=6x-2

300

What are the coordinates of the points on the graph f(x)=x³-7x where the slope of the tangent is 5

(2,-6) and (-2, 6)

400

The values of a and b for f(x)=ax³+bx²+3x-2 given that f(2)=10 and f'(-1)=14

what is 2 and -5/2

Concepts

100

The process of finding the derivative is called...

differentiation

200

The slope of the curve is found using...

the derivative

300

The first principles formula starts with the limit as h tends towards...

0

400

If average rate of change is represented by a chord, then instantaneous rate of change is represented by a...

tangent line