How can calculus be used with functions that are not powers of $x$?

Key questions

  1. 1

    How can trigonometric functions be differentiated and integrated?

  2. 2

    Is the derivative function always different from the original function?

  3. 3

    How can exponentials and logarithmic functions be differentiated and integrated?

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Resource type Title
Scaffolded task Rotating derivatives
Scaffolded task To the limit
Problem requiring decisions Estimating gradients


Resource type Title
Building blocks Similar derivatives
Building blocks Sine stretching
Building blocks Trig gradient match
Many ways problem Sine on the dotted line
Many ways problem Trigsy integrals
Scaffolded task Stretching an integral
Food for thought Inverse integrals
Food for thought Two for one
Resource in action Inverse integrals - teacher support

Review questions

Title Ref
Can the integral of $\sin(\sin t)$ be zero? R6622
Can we find the area between $\sin x$ and $\sin 2x$? R9184
Can we find the turning points on the curve $y = \sin x + \cos x$? R6938
Can we find the velocity and acceleration of this particle? R8071
Can we find this integral involving the floor function? R7106
Is this product of integrals positive or negative? R7616
What is the area under the curve $y = \cos x - \sin x +2$? R8679
Where do the curves $y=\sin 2x$ and $y=\sin x$ cross? R7074