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Use chain rule and implicit differentiation to find dy/dx for y^3 = 1 + 3*x^2, then show that they are equal

When using the Chain Rule, it is best to put our equal in a form where there are no operations performed on the subject. i.e. y = (1 + 3*x²)^1/3

Then to help make it clear what...

Answered by Joshua P. • Maths tutor

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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 denomni...

Answered by Simon C. • Maths tutor

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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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