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How do you find the first order derivative of sin(x) and cos(x) functions?

The general rules are:d(sin x)/ dx = cos xd(cos x)/ dx = -sinxHowever, if you have a constant k in the function such as y = sin(kx), the derivative will be dy/dx = kcos(kx). (For y = cos(kx), the derivati...

Answered by Niusha S. • Maths tutor

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Find the x-coordinates of any stationary points of the equation y = x^3 - 2x + 4/x

y = x^3 - 2x +4/x, dy/dx = 3x^2 - 2 - 4/(x^2) = 0 at the stationary points, 3x^4 - 2x^2 - 4 = 0, substitute in u for x^2: 3u^2 - 2u - 4 = 0, use the quadratic formula: u = (-(-2) +- sqrt((-2)^2 - 4

Answered by • Maths tutor

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Curve C has equation 4x^2- y^3 - 4xy +2^y = 0 , point P (-2, 4) lies on C, find dy/dx at the point P

Use implicit differentiation 1) 8x - 3y^2dy/dx - 4y - 4xdy/dx +2^y*ln2 * dy/dx = 0 You then sub in the points P (-2,4) 2) 8(-2) - 3(4)^2 *dy/dx - 4(4) - 4(-2) *dy/dx + 2^(4) *ln2 * dy/dx = 0 Rear...

Answered by Fernando F. • Maths tutor

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What is greater e^pi or pi^e?

Let a^b >b^a, then blna>alnb, (lna)/a > (lnb)/b, Thus we graph the function (lnx)/x, We can see that this tends towards 0 as x tends towards infinity. We can also see that it is increasing from x...

Answered by • Maths tutor

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What is integration?

when integrating a function which describes a certain curve, the answer we get gives us the area under the curve. When integrating a general polynomial you simply add 1 to the power and divide by the new ...

Answered by Jacob G. • Maths tutor

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