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

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

iGCSE (2021 Edition)

11.03 Differentiating x^n for non-integer n

Interactive practice questions

Determine the derivative of $y=x^{\frac{6}{5}}$y=x65.

Easy

< 1min

Determine the derivative of $y=x^{0.6}$y=x0.6.

Easy

< 1min

Differentiate $y=x^{-\frac{1}{5}}$y=x−15 with respect to $x$x. Express your answer in positive index form.

Easy

2min

Find the derivative of $y=x-x^3+\sqrt[8]{x}+3$y=x−x3+⁸√x+3.

Give your answer with positive indices.

Easy

2min

Outcomes

0606C14.2

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

0606C14.3A

Use the derivatives of the standard functions x^n (for any rational n), together with constant multiples, sums and composite functions.

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