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Maths

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How do you find an angle in a right-angled triangle when you are given two of its side's lengths?

You must first identify the names of the two sides in relation to the angle you are trying to find out. The technique "sohcahtoa" is generally very helpful in working this out. This abbreviat...

Answered by Toby W. • Maths tutor

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How do we differentiate y = arctan(x)?

Step 1: Rearrange y = arctan(x) as tan(y) = x.

Step 2: Use implicit differentiation to differentiate this with respect to x, which gives us:

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Answered by Solly C. • Maths tutor

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How do you find the integral of sin^2(x) dx?

Sin^2(x) cannot be integrated in its current form so you must use trigonometric identities to change sin^2(x) into something else.

Use the formula for cox(2x): cos(2x)=cos(x+x)=cos^2(x)-s...

Answered by Chloe W. • Maths tutor

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A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.

a.) dy/dx+10x^4+20x^3

d^2y/dx^2=40x^3+60x^2

b.)sub in x=-1 to dy/dx=10(-1)^4+20(-1)^3

=-10

therefore, decreasing

Answered by Alexandra F. • Maths tutor

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Explain the Chain Rule

The chain rule is used to differentiate composite functions, ie "a function of a function". In this case we have an outer function and an inner function. For example

Differentia...

Answered by Alex C. • Maths tutor

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