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Given y=2x(x^2-1)^5, show that dy/dx = g(x)(x^2-1)^4 where g(x) is a function to be determined.

y=2x(x 2 -1) 5 --> y=uv, where u=2x; v=(x 2 -1) 5 --> thus product rule required.u'=2v'=10x(x 2 -1) 4 Product rule: dy/dx = uv' + v'uTherefore: dy/dx = 2x(10x(x 2 -1) 4 ) + 2(x 2 -1) 5 g(x) = (22x 2 -2)
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Answered by Sean H. • Maths tutor
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Find the finite area enclosed between the curves y=x^2-5x+6 and y=4-x^2

Starting by factorising the curve equations: the first one factorises to y = (x-3)(x-2) and the second one becomes y=(2-x)(2+x). From this, a rough sketch of the curves can be drawn and it can be seen that f...
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Answered by Ruby N. • Maths tutor
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Expand (1+2x)(4x+3)

Deploy the FOIL method; F irst O uter I nner L ast(1+2x)(4x+3) = 4x+3+8x^2+6x = 8x^2 + 10x + 3
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Answered by Ben R. • Maths tutor
3466 Views

Work out 2 1/7 + 1 1/4.

It is important to notice that this is the addition of two mixed fractions which firstly needs to be changed into improper fractions. Take 2 1/7 - first multiply the denominator by the whole number to give 1...
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Answered by Georgia H. • Maths tutor
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Solve the simultaneous equation: 2x - 5y = 9 , x + 6y = -4

First multiply the second equation by 2, so it becomes 2x + 12y = -8. Then subtract the second equation from the first one which gives (2x - 2x) + (-5y - 12y) = (9 - -8), -17y = 17. Therefore y = -1. Plug th...
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Answered by Anagh C. • Maths tutor
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