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1EDEXCEL C1 June 2014 Q7
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2OCR C1 June 2013 Q3
It is given that f(x) = 6/x^2 + 2x. (i) Find f'(x). [3] (ii) Find f''(x). [2]
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3EDEXCEL C1 January 2013 Q11
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4OCR C1 January 2012 Q6
Given that f(x) = 4/x - 3x + 2, (i) find f'(x), [3] (ii) find f''(1/2). [4]
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5EDEXCEL C1 January 2012 Q1
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6EDEXCEL C1 June 2011 Q2
Given that y = 2x^5 + 7 + 1/x^3, x not equal to 0, find, in their simplest form, (a) dy/dx, (3) (b) the integral of y with respect to x. (4)
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7EDEXCEL C1 January 2011 Q11
The curve C has equation y = (1/2)x^3 - 9x^(3/2) + 8/x + 30, x > 0. (a) Find dy/dx. (4) (b) Show that the point P(4, -8) lies on C. (2) (c) Find an equation of the normal to C at the point P, giving your answer in the form ax + by + c = 0, where a, b and c are integers. (6)
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8EDEXCEL C1 June 2010 Q7
Given that y = 8x^3 - 4sqrt(x) + (3x^2 + 2)/x, x > 0, find dy/dx. (6)
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9EDEXCEL C1 January 2010 Q1
Given that y = x^4 + x^(1/3) + 3, find dy/dx. (3)
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10EDEXCEL C1 June 2009 Q3
Given that y = 2x^3 + 3/x^2, x not equal to 0, find (a) dy/dx (3) (b) the integral of y with respect to x, simplifying each term. (3)
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11EDEXCEL C1 June 2009 Q9
f(x) = (3 - 4sqrt(x))^2 / sqrt(x), x > 0. (a) Show that f(x) = 9x^(-1/2) + Ax^(1/2) + B, where A and B are constants to be found. (3) (b) Find f'(x). (3) (c) Evaluate f'(9). (2)
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12EDEXCEL C1 January 2009 Q6
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13Edexcel A Level June 2022 Paper 2 Q4
Given that y = 2x^2, use differentiation from first principles to show that dy/dx = 4x. (3)
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14EDEXCEL C1 January 2008 Q5
(a) Write (2sqrt(x) + 3)/x in the form 2x^p + 3x^q where p and q are constants. (2) Given that y = 5x - 7 + (2sqrt(x) + 3)/x, x > 0, (b) find dy/dx, simplifying the coefficient of each term. (4)
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15Edexcel A Level June 2023 Paper 1 Q12
y = sin(x), where x is measured in radians. Use differentiation from first principles to show that dy/dx = cos(x). You may use without proof the formula for sin(A + B) or sin(A - B), and assume that as h tends to 0, sin(h)/h tends to 1 and (cos(h) - 1)/h tends to 0. (5)
16Edexcel A Level June 2024 Paper 2 Q1
y = 4x^3 - 7x^2 + 5x - 10. (a) Find in simplest form (i) dy/dx (ii) the second derivative d^2y/dx^2 (3) (b) Hence find the exact value of x when d^2y/dx^2 = 0. (2)
