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)

11.19 Differentiating composite functions

Interactive practice questions

Differentiate $y=e^{\sin x}$y=esinx.

Easy

< 1min

Consider the equation $y=e^{\tan\left(-6x\right)}$y=etan(−6x).

Medium

2min

Find the derivative of $\cos\left(x\right)e^{5x}$cos(x)e5x. You may use the substitutions $u=\cos\left(x\right)$u=cos(x) and $v=e^{5x}$v=e5x. Leave your answer in factorised form.

Medium

2min

Differentiate $y=\sin\left(x\right)e^x$y=sin(x)ex. Give your answer in factorised form.

Medium

1min

Outcomes

0606C14.3B

Use the derivatives of the standard functions sinx, cos x, tan x, together with constant multiples, sums and composite functions.

0606C14.3C

Use the derivatives of the standard functions e^x, ln x, together with constant multiples, sums and composite functions.

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