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Why is the derivative of inverse tan(x) 1/(1+x^2)?

This can be proven by understanding tan(x) and it's inverse as functions, using implicit differentiation, subsitution and by recognising trigonometric identities (or being able to prove them from first princ...
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Answered by Neel G. • Maths tutor
6999 Views

Find the area beneath the curve with equation f(x) = 3x^2 - 2x + 2 when a = 0 and b = 2

This question is an example of integrating to find the area underneath a curve between two points. We begin by intergrating the equation. Firstly, to integrate 3x 2 we increase the indice/power by one unit a...
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Answered by Thomas C. • Maths tutor
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Use implicit differentiation to find dy/dx of a curve with equation x^3 + yx^2 = y^2 + 1.

Begin by differentiating each term w.r.t x: d/dx(x^3) + d/dx(yx^2) = d/dx(y^2) + d/dx(1). the terms x^3 and 1 are simple enough to start of with: d/dx(x^3) = 3x^2 and d/dx(1) = 0. Next use the chain rule for...
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Answered by Marlon H. • Maths tutor
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Sketch the line y=x^2-4x+3. Be sure to clearly show all the points where the line crosses the coordinate axis and the stationary points

From the equation we can see the the line in a positive quadratic graph. In order to find the points where the line crosses the x axis we must let y=0 and solve for x. We can then use either inspection, comp...
MS
Answered by Matthew S. • Maths tutor
5705 Views

Integrate (x^2+4x+13)/((x+2)^2)(x-1) dx by using partial fractions

Express (x 2 +4x+13) / (x+2) 2 (x-1) as partial fractions. (x 2 +4x+13) / (x+2) 2 (x-1) = a/(x+2) +b/(x+2) 2 +c/(x-1) where a, b and c are constants to be found. Multiplying by the denominator, we get (x 2 +...
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Answered by Donny W. • Maths tutor
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