Book a Demo

Topics

11. Differentiation

11.01 Tangents and the derivative

11.02 Differentiating x^n for integer n

11.03 Differentiating x^n for non-integer n

11.04 Tangents and normals

11.05 Chain rule

11.06 Product rule

11.07 Quotient rule

11.08 Using the first derivative

11.09 Using the second derivative

Lesson

Worksheet

Practice

11.10 Graphing techniques using calculus

11.11 Optimisation problems

11.12 Defining e and the natural logarithm

11.13 Differentiating exponential functions

11.14 Applications of the differentiation of exponential functions

11.15 Differentiating logarithmic functions

11.16 Applications of the differentiation of logarithmic functions

11.17 Differentiating trigonometric functions

11.18 Applications of the differentiation of trigonometric functions

11.19 Differentiating composite functions

11.20 Small increments and approximations

11.21 Kinematics

11.22 Related rates of change

Book a Demo

iGCSE (2021 Edition)

11.09 Using the second derivative

Lesson

Worksheet

Practice

Interactive practice questions

Suppose $y=5x^8$y=5x8.

Find $\frac{dy}{dx}$dydx.

Find $\frac{d^2y}{dx^2}$d2ydx2.

Find $\frac{d^3y}{dx^3}$d3ydx3.

Find $\frac{d^4y}{dx^4}$d4ydx4.

Find $\frac{d^5y}{dx^5}$d5ydx5.

Easy

2min

Suppose $y=\frac{2}{x^5}$y=2x5.

Easy

2min

$y=-2x^4+4x^3-7x^2+8x-9$y=−2x4+4x3−7x2+8x−9

Easy

5min

Find the second derivative, $f''\left(x\right)$f′′(x), of $f\left(x\right)=x^{\frac{1}{7}}$f(x)=x17.

Easy

1min

Outcomes

0606C14.2

Use the notations f'(x), f''(x), dy/dx, d^2y/dx^2 [=d/dx(dy/dx)].

0606C14.5B

Apply differentiation to stationary points.

0606C14.6

Use the first and second derivative tests to discriminate between maxima and minima.

11.09 Using the second derivative

Interactive practice questions

Outcomes

0606C14.2

0606C14.5B

0606C14.6

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