Problem Sheets
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Differentiation Problem Sheet
In this problem sheet we differentiate general polynomials - functions of the form x^n.
We heavily advise you first watch our Differentiation Video
Stationary Points Problem Sheet
In this problem sheet we use differentiation to solve stationary point problems.
We heavily advise you first watch our Stationary Points Video
Proof of the derivative of tan(x)
Here we prove the derivative of tan(x) by first principles through approximations.
Watch our video first Differentiating sin(x), cos(x) and tan(x)
Complete Proof of the derivative of sin(x) and cos(x)
In this paper we go through a complete proof of the derivative of sin(x) and cos(x) without the use of approximations.
Product Rule problem sheet
In this problem sheet we utilise the product and quotient rule to differentiate functions
We strongly advise you first watch our Product and Quotient Rule video
Chain Rule problem sheet
In this paper we prove the derivative of tan(x) is sec^2(x) by first principles through approximations.
We advise you first watch our video on Chain Rule
Integration Problem Sheet
In this problem sheet we go through integration examples and explain why the area under the curve can be negative
We heavily advise you first watch our Integration video
Integration by parts Problem Sheet
In this problem sheet we go through integration by parts examples, including a special one, and explain why we don’t need a constant for integration by parts.
We strongly advise you first watch our Integration by Parts video
Integration by substitution PS
In this problem sheet we go through integration by substitution examples, including definite integrals and explain what to actually substitute.
We strongly advise you first watch our Integration by substitution video