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Differentiate f(x)= x^3 + x^(1/3)-2

f'(x)= 3x^2+1/3x^(-2/3)

To differentiate you need to multiply the coefficant of the x dependent terms by the powers and then the power of x goes down by one.

For example: differentiate f(x)...

Answered by Jathursa R. • Maths tutor

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Integrate 10x(x^1/2 - 2)dx

First, expand the brackets. This will give us 10x^3/2 - 20x. Now to integrate this expression we have to increase the power of each term by one and then divide them by the number which becomes the new pow...

Answered by Giorgia S. • Maths tutor

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A curve has parametric equations -> x = 2cos(2t), y = 6sin(t). Find the gradient of the curve at t = π/3.

First we need to find the derivatives of x and y in terms of t. dx/dt can be found using the chain rule. Differentiating the inside of the bracket gives us 2. Multiplying the outside gives -2sin(2t) (Deri...

Answered by Matvei M. • Maths tutor

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How do I remember the common values of cosx, sinx and tanx?

To remeber the equations us SOH CAH TOA. This is Sinx = Opposite/Hypotenuse, Cos x = Adjacent/Hypotenuse and Tanx = Opposite/Adjacent. For values x=pi/3 and x=pi/6 always start by drawing an equilateral o...

Answered by Becky L. • Maths tutor

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Let y be a function of x such that y=x^3 + (3/2)x^2-6x and y = f(x) . Find the coordinates of the stationary points .

y = x³ + 1.5x²-6x Hence, dy/dx = 3x² + 3x - 6 Solve to find x when dy/dx = 0 as gradient is zero at stationary points Substitute the vaules for x back into y to find y co...

Answered by Michael C. • Maths tutor

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