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Differentiation

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Question 491

A curve has equation

y2=ye3x+2x y^2 = y e^{3x} + 2x y2=ye3x+2x
a.

Show that

dydx=3ye3x+22y−e3x \frac{dy}{dx} = \frac{3y e^{3x} + 2}{2y - e^{3x}} dxdy​=2y−e3x3ye3x+2​
[4]
b.

The curve crosses the yyy-axis at the origin (0,0)(0, 0)(0,0) and at a second point PPP. The tangent to the curve at the origin and the tangent to the curve at PPP meet at the point RRR. Find the coordinates of RRR.

[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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