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A curve has parametric equations x= 2sin(t) , y= cos(2t) + 2sin(t) for -1/2 π≤t≤ 1/2π , show that dy/dx = - 2sin(t)+ 1

A parametric equation is where both x and y are expressed separately, in terms of a parameter (t). In order to differentiate them we must use the chain rule, which here would be dy/dx= dy/dt ÷ dx/dt. The ...

Answered by Katie L. • Maths tutor

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find the diffrential of 3sin2x+4cos2x

dy/dx=6cos2x-8sin2xExplanation: cos x difrentiates to -sinx, we must times the coefficient of cos2x,(4) , by the differential of 2x (ie 2), giving -(4x2)sin2x.Similarly, sinx differentiates cosx, so using...

Answered by Amy C. • Maths tutor

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A curve has equation y = e^(3x-x^3) . Find the exact values of the coordinates of the stationary points of the curve and determine the nature of these stationary points.

In order to find the stationary points we need to find the first derivative, set it to 0 and solve for x. We can then use this value to find the value for y.y = e^{(3x-x^3)}We know for the derivat...

Answered by Philip M. • Maths tutor

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Find the derivative of x(x+3)^5

First we use the product rule, so we multiply x by the derivative of (x+3)⁵. To find the derivative of (x+3)⁵ we use the chain rule. So we have 5(x+3)⁴. So the first part...

Answered by John Y. • Maths tutor

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