Differentiation

Question 1

Differentiate y=10x^3

Answer 1

Dy/dx = 30x^2

Question 2

To find rate of change…

Answer 2

Differentiate then sub in value for letter and solve.

Question 3

Find the equation of a tangent

Answer 3

Differentiate and sub in x point to find the gradient. Then using point and this gradient, get the equation.

Question 4

Increasing and Decreasing Curves

Answer 4

A curve is increasing when dy/dx > 0.

Decreasing when dy/dx < 0

Question 5

Finding Stationary Points (Optimisation)

Answer 5

Differentiate equation and make equal to zero, solve for some x values. Put on a nature table, label and find lower and higher values. Sub into the dy/dx to find positive, zero or negative and determine the shape. Find stationary points by subbing x value into original equation.

Question 6

The Chain Rule

Answer 6

Multiply bracket by power, take one off power, multiply by inner derivative.

Question 7

Graphs of Derivatives Progression Rules

Answer 7

Quartic > Cubic > Quadratic > Linear.

Question 8

Drawing Graphs of Derivatives

Answer 8

Stationary points become roots and splits into sections. If decreasing curve, below x axis. If increasing curve, above x axis.