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Differentiation

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Question 3

a(i).

Differentiate with respect to $x$ : $e^{3x}(\sin x + 2 \cos x)$ .

[3]

a(ii).

Differentiate with respect to $x$ : $x^3 \ln (5x + 2)$ .

[3]

Given that $y=3x2+6x−7(x+1)2,x≠−1\displaystyle y = \frac{3x^2 + 6x - 7}{(x + 1)^2}, x \neq -1$ , show that $dydx=20(x+1)3\displaystyle \frac{dy}{dx} = \frac{20}{(x + 1)^3}$ .

[5]

Hence find $d2ydx2\displaystyle \frac{d^2y}{dx^2}$ and the real values of $x\,$ for which $d2ydx2=−154\displaystyle \frac{d^2y}{dx^2} = -\frac{15}{4}$ .

[3]

Markscheme

Differentiation Questions

A Level
Old Maths
Differentiation

14 exam-style questions on Edexcel A Level Old Maths Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

Differentiation

Question bank

Differentiation

Medium

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Question 3

a(i).

Differentiate with respect to $x$ : $e^{3x}(\sin x + 2 \cos x)$ .

[3]

a(ii).

Differentiate with respect to $x$ : $x^3 \ln (5x + 2)$ .

[3]

Given that $y=3x2+6x−7(x+1)2,x≠−1\displaystyle y = \frac{3x^2 + 6x - 7}{(x + 1)^2}, x \neq -1$ , show that $dydx=20(x+1)3\displaystyle \frac{dy}{dx} = \frac{20}{(x + 1)^3}$ .

[5]

Hence find $d2ydx2\displaystyle \frac{d^2y}{dx^2}$ and the real values of $x\,$ for which $d2ydx2=−154\displaystyle \frac{d^2y}{dx^2} = -\frac{15}{4}$ .

[3]

Markscheme

Differentiation Questions

A Level
Old Maths
Differentiation

14 exam-style questions on Edexcel A Level Old Maths Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.