Differentiation
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Question 245
The diagram shows the curve with equation x2−2xy+4y2−192=0x^2 - 2xy + 4y^2 - 192 = 0x2−2xy+4y2−192=0
a.[3]
Show that dydx=x−yx−4y\displaystyle \frac{dy}{dx} = \frac{x - y}{x - 4y}dxdy=x−4yx−y
b.[7]
At the point P P\,P on the curve the tangent to the curve is parallel to the yyy-axis and at the point Q Q\,Q on the curve the tangent to the curve is parallel to the xxx-axis. Show that the exact distance PQPQPQ, is k5 k\sqrt{5}\,k5 where k k\,k is a rational number to be determined.
Differentiation Questions
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.