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A curve has the equation y = 2x cos(3x) + (3x^2-4) sin(3x). Find the derivative in the form (mx^2 + n) cos(3x)

y = 2x cos(3x) + (3x 2 -4) sin(3x) dy/dx = (2x x -sin(3x) x 3) + (2 x cos(3x)) + (6x sin(3x)) + ((3x 2 -4) cos(3x) x 3) dy/dx = -6x sin(3x) + 2 cos (3x) + 6x sin(3x) + (9x 2 -12) cos(3x) dy/dx = (9x 2 -12 + ...
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Answered by Thomas L. • Maths tutor
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What is the nth term of the sequence 5, 7, 9, 11....

Difference between each number is +2Therefore the sequence is 2n + C When n = 1 the value is (2x1) + C = 2 + C = 5C = 36 nth term is 2n + 3 CHECK 3rd term should be (2x3) + 3 = 6 + 3 = 9 Which is correct
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Answered by Thomas L. • Maths tutor
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Find the value of x which satisfies the following equation 3 x2 + 6 x + 3 = 0

3 x 2 + 6 x + 3 = 0 . .../3 x 2 + 2 x + 1 = 0(x+1) 2 =0x+1=0x=-1PROOF3 (-1) 2 + 6 (-1) + 3 = 0
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Answered by Catherine T. • Maths tutor
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Find the antiderivative of the function f(x)=cos(2x)+5.

In order to find the antiderivative of the function we're given, we first have to study the general structure of the function. This function consists of a sum between cos(2x) and 5. Therefore, we have : F(x)...
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Answered by Tutor149135 D. • Maths tutor
5686 Views

Find the stationary points of the function f(x) = x^3 - 27x and determine whether they are maxima or minima

A stationary point occurs when the first derivative of the function = 0. The first derivative of f(x) is df(x)/dx = 3x^2 - 27Setting this to zero gives 3x^2 - 27 = 0 -> x = +/- 3 To find whether it is a m...
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Answered by Iman S. • Maths tutor
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