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differentiate y=(3x)/(x^2+6)

using the quotent ruledy/dx= (3(x^2+6)-3x(2x))/(x^2+6)^2dy/dx=3(x^2+6-2x^2)/(x^2+6)^2dy/dx=(18-3x^2)/(x^2+6)^2
MS
Answered by Michael S. • Maths tutor
4473 Views

The curve C has the equation: y=3x^2*(x+2)^6 Find dy/dx

To find dy/dx, we must use a combination of the Product Rule and the Chain Rule. If we let 3x^2=u and (x+2)^6=v, the Product Rule tells us that (uv)' = uv'+vu' u'=6x, but to find v' we need to use the Chain ...
SH
Answered by Sam H. • Maths tutor
4400 Views

How can I understand eigenvalues and eigenvectors?

A matrix is a linear transformation between vector spaces. Often we want to think about linear maps from an n -dimensional vector space to itself. When the vector space that we're mapping to and from is the ...
JW
Answered by James W. • Maths tutor
4143 Views

If I throw a ball vertically upwards with a velocity of 15 m/s and we assume the gravitational acceleration is 10 m/s^2. Draw the distance-time, and velocity-time graphs, how long is the ball in the air before it returns to the point I threw it from?

We will need a SUVAT equations, so first fill in what information we have:S = 0 (the point where the ball returns to the start)U = +15 m/sV = -15 m/s (from graph)A = -10 m/s (important that this is the oppos...
BF
Answered by Barnaby F. • Maths tutor
4244 Views

Find the equation of the tangent line to the parabola y=x^2+3x+2 at point P(1, 6).

In order to find the equation of the tangent line, first we have to find its slope. To do this, we take the first derivative of the function. In this particular case, we just need to apply the power rule (if...
BA
Answered by Boris A. • Maths tutor
6242 Views