9709 · topic questions
Differentiation
12 past-paper questions on Differentiation
The equation of a curve is y = e^(sinx) / cos²x for 0 ≤ x ≤ 2π. Find dy/dx and hence find the x-coordinates of the stationary…
A curve is defined by the parametric equations x = 4 cos²t, y = √3 sin 2t, for values of t such that 0 < t < π/2. Find the…
The equation of a curve is ye^(2x) + y²e^x = 6. Find the gradient of the curve at the point where y = 1.
The diagram shows the graph of y = 5 sin 2x cos²x for 0 ≤ x ≤ ½π and its maximum point M. Find the exact x-coordinate of M.
Find the exact coordinates of the stationary point of the curve y = e^(2x) sin2x for 0 ≤ x ≤ ½π.
A particle P moves in a straight line and passes through the point A at time t = 0. The velocity vms¯¹ of P at time t seconds is…
(a) Show that dy/dx can be expressed in the form c(3t+4) and state the value of the constant c. [5]
The diagram shows the curve y = sin2x(1+sin2x), for 0 ≤ x ≤ ¾π, and its minimum point M. The shaded region bounded by the curve…
(b) It is given that the gradient of the curve at the point (a, ln100) is m. Find the values of a and m. [4]
The diagram shows the curve y = xe^(-ax), where a is a positive constant, and its maximum point M. Find the exact coordinates of…
The equation of a curve is ln(x+y) = 3x²y. Find the gradient of the curve at the point (1,0).
Hence find the equation of the normal to the curve at the point where t = π/8. Give your answer in the form y = mx+c.
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Differentiation (9709) past-paper questions — marked instantly
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