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Differentiation

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Question 303

A curve has the equation y=ax2y = a^{x^2}y=ax2, where a a\,a is a constant greater than 1.

a.

Show that dydx=2xax2ln⁡a\displaystyle \frac{dy}{dx} = 2x a^{x^2} \ln adxdy​=2xax2lna

[3]
b.

The tangent at the point (1,a)(1, a)(1,a) passes through the point (12,0)\displaystyle (\frac{1}{2}, 0)(21​,0). Find the value of aaa, giving your answer in an exact form.

[4]
c.

Show that the curve is convex for all values of xxx.

[5]
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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