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Differentiate the following function u = Cos(x3)

u = Cos(x 3 ) To differentiate this function we will use the chain rule. Firstly we will set x 3 to another variable name such as v. So now v = x 3 . Lets differentiate this. dv/dx = 3x 2 We can now differen...
SB
Answered by Serena B. • Maths tutor
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Prove that the sqrt(2) is irrational

To do this we will assume sqrt(2) is rational , a fraction, which means: 2 1/2 = m/n ; m,n belong to integers. Also, m/n is an irreductible fraction , meaning m and n have no common divisors. 2 1/2 = m/n &lt...
JC
Answered by Joao C. • Maths tutor
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Expand and simplify 2(a + 3) + 5(a – 1)

Firstly we will start by expanding the brackets. We will do 2 a + 2 3 for the first bracket, then we will do 5 a + 5 (-1) for the second bracket which will give us 2a + 6 + 5a - 5. We will then simplify what...
SB
Answered by Serena B. • Maths tutor
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Factorise and solve x^2 - 8x + 15 = 0

In order to solve a quadratic equation by factorisation you must first find the two numbers which add up to - 8 and multiply to get 15. We can do this by trial and error - first listing all of the pairs of f...
LM
Answered by Lucy M. • Maths tutor
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Differentiate y = 7(x)^2 + cos(x)sin(x)

This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rule: ...
EC
Answered by Edward C. • Maths tutor
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