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Given that y= 1/ (6x-3)^0.5 find the value of dy/dx at (2;1/3)

Let u=6x-3 , then y=u^-0.5hence, du/dx=6 and dy/du= -0.5u^-3/2then, as dy/dx =dy/du * du/dx dy/dx=(-0.5u^-3/2 )*6= -3(6x-3)^-3/2substitute x=2 to give the required value required value : -1/9
PN
Answered by Polina N. • Maths tutor
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Find an equation for the straight line connecting point A (7,4) and point B(2,0)

In this question we will use the fact we know a straight line can be written in the form (y-y 1 )=m(x-x 1 ). Where m is the gradient and (x 1 ,y 1 ) is a point on the line. We already have a point A so can s...
HM
Answered by Hannah M. • Maths tutor
4814 Views

What are the uses of derivatives in algebra?

Derivatives can be used to work out rates of change of non-linear systems which are encountered everyday. Moreover derivatives allow us to describe the shape of a function.
AM
Answered by Amdadullah M. • Maths tutor
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Where does the circle equation come from?

equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r. Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and (a, b) i...
AB
Answered by Ashwin B. • Maths tutor
4514 Views

How would I find the indefinite integral of x*cos(x) dx

Use integration by parts, by setting u=x and cos(x)=dv/dx. The final result should be xsinx + cosx + c.
ES
Answered by Ed S. • Maths tutor
4839 Views