Top answers

The curve C has equation y = 3x^4 – 8x^3 – 3. Find dy/dx.

To find dy/dx, the differential, of any function... you must times the coefficient of each variable of x by its power, then reduce the power by one. Using this information we can work out that 3x^4 turns to ...
JC
Answered by Joseph C. • Maths tutor
5028 Views

How do I determine the domain and range of a composite function, fg(x) ?

Firstly I would state the rule that for any composite function fg, its domain is always the domain of g. If the student would like to know why this is the case, I would simplify the expression fg(x) to f(g(x...
RS
Answered by Rhys S. • Maths tutor
11776 Views

The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.

We start off by differentiating the equation implicitly which will give us:2(x-y) -2(x-y)dy/dx = 6 + 5dy/dxThen we rearrange to get dy/dx on it's own:dy/dx = (2x-2y-6)/(2x-2y+5) For the second part of the qu...
JM
Answered by Jake M. • Maths tutor
3829 Views

integral of xe^-x dx

Using integration by parts by letting u=x and dv/dx=e^-x. this implies that du/dx=1 and v=-e^-xThe By Parts formulae is u.v - integral(v.du/dx) = -xe^-x - integral(-e^-x).1 dx = -xe^-x + integral(e^-x) dx = ...
BK
Answered by Brandon K. • Maths tutor
7972 Views

The gradient of a curve is given by dy/dx = 3 - x^2. The curve passes through the point (6,1). Find the equation of the curve.

Since we differentiate a function to find the gradient of a curve at any point, we need to reverse that to find the equation of the curve. We do this by integrating with respect to x:If you have a constant (...
DN
Answered by Darya N. • Maths tutor
10857 Views