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Differentiation

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Question 84

A contour of the magnetic potential U U\,U in a specialized laboratory setup is modeled by the curve with equation

x5y+4xy5=130 x^5 y + 4x y^5 = 130 x5y+4xy5=130
a.

Prove that the curve does not intersect the coordinate axes.

[2]
bi.

Show that

dydx=−5x4y+4y5x5+20xy4 \frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4} dxdy​=−x5+20xy45x4y+4y5​
[3]
bii.

Prove that the curve has no stationary points.

[3]
biii.

In the case when x>0x > 0x>0, find the equation of the tangent line to the curve at the point where y=2y = 2y=2. Give your answer in the form ay+bx=cay + bx = cay+bx=c, where a,b,c a, b, c\,a,b,c are integers.

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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