C3 Differentiation Worksheet C . The tangent at the point c where x = 1 meets the x axis at the point a. Solomon press c3 differentiation worksheet b 1 a find an equation for the normal to the curve y = 2 5 x + 1 10 ex at the point on the curve where x = 0, giving your answer in the form ax + by + c = 0, where a, b and c are integers.
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Solomon press c3 differentiation worksheet i 1 a curve has the equation x = y. (3) 2 a curve has the equation y = xe−2x. 2 differentiate each of the following with respect to x and simplify your answers.
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2 y y = 5ex − 3 ln x p q o r x the diagram shows the curve with equation y =. C3 differentiation page 10 example 4 the curve c has equation 7 y 4x ln4x 2, where x > 0. Model t = 3, m = 764 (3sf) 2 2 9 x x − − model b: X = 0 d d m t = 1500(3t + 2)−2 × 3 = 2 4500 (3 2)t + ∴ (0, ln 9) t = 3, d d m t = 37.2 c x = 1, y = ln 8 = ln 23 = 3 ln 2 ∴ increasing at 37.2 tonnes yr−1 (3sf)
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10(2x 2− 3)4 = 0 sp: Solomon edexcel worksheets and answers for the c3 module. T = 3, m = 732 (3sf) b sp: 2 verify the relationship d d y x × d d x y = 1 when a 2y = e x − 1, b y = x3 + 2, c x = ln y. Solomon press.
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Solomon press c3 differentiation worksheet e 1 given that f(x) = x(x + 2)3, find f ′(x) a by first expanding f(x), b using the product rule. Y = x 3x + 2 = −c3x when x = 0, y = 0 ∴ passes through origin x = 1 3 − ∴ (1 3 − , 1) 3 ap (−3,.
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Find the derivatives of trigonometric, logarithmic and exponential functions. C3 1 differentiation c3 specifications. 10(2x 2− 3)4 = 0 sp: A xy = 4x3 + e xb y = 7e − 5x2 + 3x c y = ln x + x52 d y = 5ex + 6 ln x e y = 3 x + 3 ln x. X =.
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(3) 2 a curve has the equation y = xe−2x. A find the gradient of c at the point (1, 1 4). By the end of this unit you should be able to : 10(2x 2− 3)4 = 0 sp: C3 1 differentiation c3 specifications.
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T = 3, m = 732 (3sf) b sp: A 3y = x b y = 4x − x2 c y = 2x2 − 8x + 3 d y = 3 x + 2 2 find the gradient of each curve at the given point. A 4y = (3x − 1. 2 verify the relationship d d y x ×.
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T = 3, m = 764 (3sf) 2 2 9 x x − − model b: T = 3, m = 732 (3sf) b sp: A 4 13 x − x b e 4 x x − c 1 23 x x + + d ln 2 x x e 2 2 x − x f 32 x x +.
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2 differentiate each of the following with respect to x and simplify your answers. Y = x 3x + 2 = −c3x when x = 0, y = 0 ∴ passes through origin x = 1 3 − ∴ (1 3 − , 1) 3 ap (−3, 0), q (1, 0) 4 ad d y x = 1 × 41x.
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A xy = 4x3 + e xb y = 7e − 5x2 + 3x c y = ln x + x52 d y = 5ex + 6 ln x e y = 3 x + 3 ln x. T = 3, m = 764 (3sf) 2 2 9 x x − − model b: (3) 2 a curve has the.
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Solomon press c3 differentiation worksheet h 1 differentiate with respect to x a cos x b 5 sin x c cos 3x d sin 1 4 x e sin (x + 1) f cos (3x − 2) g 4 sin (π 3 − x) h cos (1 2 x + π 6) i sin2 x j 2 cos3 x k.
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The tangent at the point c where x = 1 meets the x axis at the point a. Work will also include turning points and the equations of tangents and C write down d d y x in terms of x. 2 differentiate each of the following with respect to x and simplify your answers. A y = x(2x −.
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(3) 2 a curve has the equation y = xe−2x. D hence verify that for this curve, d d y x = 1 d d x y. Solomon press c3 differentiation worksheet b 1 a find an equation for the normal to the curve y = 2 5 x + 1 10 ex at the point on the curve where.
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2 differentiate each of the following with respect to x and simplify your answers. Prove that the x coordinate of a is 9 ln4 13. T = 3, m = 764 (3sf) 2 2 9 x x − − model b: A xxe b x(x + 1)5 c x ln x d x2(x − 1)3 e 3x ln 2x 4f.
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T = 3, m = 764 (3sf) 2 2 9 x x − − model b: D hence verify that for this curve, d d y x = 1 d d x y. B express the equation of the curve in the form y = f(x). The tangent at the point c where x = 1 meets the x axis.
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C3 differentiation worksheet k 1 the curve c has equation y = 1 4x − ln x. 2 verify the relationship d d y x × d d x y = 1 when a 2y = e x − 1, b y = x3 + 2, c x = ln y. Solomon press c3 differentiation worksheet h 1 differentiate with.
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Solomon press c3 differentiation worksheet h 1 differentiate with respect to x a cos x b 5 sin x c cos 3x d sin 1 4 x e sin (x + 1) f cos (3x − 2) g 4 sin (π 3 − x) h cos (1 2 x + π 6) i sin2 x j 2 cos3 x k.
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A 4 13 x − x b e 4 x x − c 1 23 x x + + d ln 2 x x e 2 2 x − x f 32 x x + g 2 2 e 1e x − x h 21 3 x x + − 3 find d d y x, simplifying your answer in.
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T = 3, m = 732 (3sf) b sp: A xy = 4x3 + e xb y = 7e − 5x2 + 3x c y = ln x + x52 d y = 5ex + 6 ln x e y = 3 x + 3 ln x. Model t = 3, m = 764 (3sf) 2 2 9 x x.
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Use chain rule to find the derivative of composite functions. By the end of this unit you should be able to : Find the derivative of products and quotients. 2 differentiate each of the following with respect to x and simplify your answers. C3 differentiation worksheet k 1 the curve c has equation y = 1 4x − ln x.
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2 2 9 x x − − = 0 b model a: C3 and c4 differentiation revision. (3) 2 a curve has the equation y = xe−2x. The tangent at the point c where x = 1 meets the x axis at the point a. Model t = 3, m = 764 (3sf) 2 2 9 x x − −.
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Find the derivatives of trigonometric, logarithmic and exponential functions. A 4y = 3x2 + x − 5 (1, −1) b y = x + 2x3 (−2, 0) c y = x(2x − 3) (2, 2) d y = x2 − 2x−1 (2, 3) e 2y = x + 6x + 8 (−3, −1) f y = 4x + x. 2.