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How do I simplify (1 / [1 + cos(x) ] ) + (1 / [1 - cos(x) ] )?

In order to add the fractions together, we must have a common denominator of the fractions. The simplest way to do this is to make the denominators of the equations the product of the original two denomniato...
SC
Answered by Simon C. • Maths tutor
15019 Views

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 ) which gives 4x ...
JG
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^x ...
JI
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 = -6 sin(3t) and dx/dt = 12 cos(3t). Substituing these in we have dy/dx = -6*sin(3t) 1/(12 cos(3t) which simplifie...
BS
Answered by Barnaby S. • Maths tutor
7071 Views

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 = 3x 2 - 12 = 0) From this we find that the turning points happen when x = 2, x = -2 ...
JR
Answered by Jon R. • Maths tutor
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