Differentiate y=x^2cos(x)
This is done using the product rule: dy/dx=udv/dx +vdu/dxset y=uv therefore u=x^2 v=cos(x)differentiate these with respect to x du/dx= 2x as you multiply by the power and then subtract the power by 1dv/dx= -sin(x) these are one the derivatives that have to be learnt for the examplug these values into the product rule to get the following:dy/dx= (x^2)(-sin(x)) + (cos(x))(2x)rewritten to dy/dx= 2xcos(x) - x^2sin(x)can be further simplified by factorising and taking out the x to get the final answer: dy/dx = x(2cos(x) - xsin(x))
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Related Maths A Level answers
All answers ▸Find the stationary point(s) on the curve 2xsin(x)
∫(1 + 3√x + 5x)dx
1. The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) d d y x (ii) d d 2 y x 2 (3) (b) Verify that C has a stationary point when x = 2 (2) (c) Determine the nature of this stationary point, giving a reason for your answer.
Solve, giving your answer to 3 s.f. : 2^(2x) - 6(2^(x) ) + 5 = 0