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At each point P of a curve for which x > 0 the tangent cuts the y-axis at T, and N is the foot of the perpendicular from P to the y-axis. If T is always 1 unit below N and the curve passes through the point (1,0), find the Cartesian equation of the curve.

When faced with a problem like this, it is always a good idea to draw a rough sketch of what might be going on. With the help of a diagram, we notice that PNT is a right angled triangle with part of the tang...
SP
Answered by Siddharth P. • Maths tutor
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A curve C has equation: x^3+2xy-x-y^3-20=0. Find dy/dx in terms of x and y.

First we need to make sure we understand implicit differentiation. As we are differentiating with respect to x, y has to be treated differently, this is because it could be anything from a constant to a func...
MM
Answered by Martin M. • Maths tutor
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Find the inverse of the function g(x)=(4+3x)/(5-x)

For simplicity first rewrite as y=(4+3x)/(5-x). Now swap any x for a y, and any y for an x. This leaves the equation x=(4+3y)/(5-y). Our goal is to make y the subject of the formula. Multiply both sides by (...
MM
Answered by Martin M. • Maths tutor
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The equation of curve C is 3x^2 + xy + y^2 - 4x - 6y + 7 = 0. Use implicit differentiation to find dy/dx in terms of x and y.

6x + xdy/dx + y + 2ydy/dx - 4 - 6dy/dx = 0xdy/dx + 2ydy/dx - 6dy/dx = 4 - 6x - ydy/dx (x + 2y - 6) = 4 - 6x - ydy/dx = (4-6x-y)/x+2y-6)
Answered by • Maths tutor
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Given that y =2x^3 + 3/(x^2), find a) dy/dx and b) the integral of y

a) It is useful to rewrite the equation using power rules, so we get y = 2x 3 + 3x -2 Now we can simply use the differentiation rules where we multiply the coefficient (number before x) by the power, then re...
BS
Answered by Balint S. • Maths tutor
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