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)

11.18 Applications of the differentiation of trigonometric functions

Interactive practice questions

The curve $y=-5x\sin x$y=−5xsinx passes through the point $P\left(\pi,0\right)$P(π,0).

Find the equation of the tangent at point $P$P.

Medium

6min

Consider the function $y=\frac{\sin x}{1+\cos x}$y=sinx1+cosx.

Medium

5min

Consider the function $f\left(x\right)=\cos2x-\sqrt{3}\sin2x$f(x)=cos2x−√3sin2x.

Medium

10min

Consider the function $f\left(x\right)=-4\cos3x$f(x)=−4cos3x.

Solve for $\theta$θ, the angle that the tangent at $x=\frac{\pi}{12}$x=π12 makes with the positive $x$x-axis.

Give your answer to the nearest degree.

Medium

5min

Outcomes

0606C14.3B

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

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