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A curve has the equation: x^2(4+y) - 2y^2 = 0 Find an expression for dy/dx in terms of x and y.

First of all expand the brackets in the equation. Then you can differentiate each term with respect to x. As one of the terms will be a product of x and y the product rule must be used to find the differenti...
CM
Answered by Carlotta M. • Maths tutor
4543 Views

Prove that, if 1 + 3x^2 + x^3 < (1+x)^3, then x>0

(1+x)^3 = x^3 + 3x^2 + 3x + 1 (Can be calculated straight away by binomial method or by multiplying brackets individually) if (1+x)^3 &gt; 1 + 3x^2 + x^3then: x^3 + 3x^2 + 3x + 1 &gt; 1 + 3x^2 + x^3 3x &gt; ...
VT
Answered by Vigneswaran T. • Maths tutor
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If x:y=7:4 and x + y = 88, work out the value of x – y.

Total of parts: 7+4=11therefore if we divide 88 in 11 “parts” we get each part as 8.hence if x corresponds to 7 parts then x=8X7=56 and if y corresponds to 4 “parts” y=4X8=32THEREFORE: x-y=56-32=24
GH
Answered by Georgina H. • Maths tutor
6031 Views

Differentiate y = xe^(2x).

We want to find dy/dx. We find this using the product rule by setting the functions f(x) = x and g(x) = e 2x . With these functions, we can write the equation as y = f(x)g(x), so by applying the product rule...
ML
Answered by Matthew L. • Maths tutor
34129 Views

Find the points where f(x)=x^2-5x-14 meets the x-axis and find the turning point

Set x^2-5x-14=0. So (x-7)(x+2)=0So function meets x-axis at (-2,0) and (7,0). To find turning point, differentiate function and set equal to 0.2x-5=0. So x=5/2. Substitute x=5/2 into f(x) to give y coordinat...
DB
Answered by Daanesh B. • Maths tutor
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