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A curve has the equation: x^4 + 2x -xy - y^3 - 10=0. Find dy/dx in terms of x and y.

We need to differentiate all values with respect to x. Therefore for the first two terms, multiply by the power and then subtract 1 from the original power. Therefore 4(x^4-1) + (2)(2x^2-1

Answered by John G. • Maths tutor

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A curve has equation y = e^x + 10sin(4x), find the value of the second derivative of this equation at the point x = pi/4.

Firstly, differentiate y with respect to x once to obtain the equation dy/dx = e^x + 40cos(4x). Then differentiate this resultant expression, with respect to x, to acquire a solution for (d^2)y/d(x^2) = e...

Answered by Joe I. • Maths tutor

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A function is defined parametrically as x = 4 sin(3t), y = 2 cos(3t). Find and simplify d^2 y/dx^2 in terms of t and y.

We first need to find dy/dx and we use the fact that dy/dx = dy/dt * dt/dx. So we have dy/dt = -6sin(3t) and dx/dt = 12cos(3t). Substituing these in we have dy/dx = -6*sin(3t)1/(12cos(3t...

Answered by Barnaby S. • Maths tutor

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The equation: x^3 - 12x + 6 has two turning points. Use calculus to find the positions and natures of these turning points.

To find the turning points we need to find when the differential of the equations with respect to x is equal to 0. (dy/dx = 3x² - 12 = 0) From this we find that the turning points happ...

Answered by Jon R. • Maths tutor

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