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Differentiate y=(3x-1)/(2x-1)

First, recognise that the function is a fraction and recall the quotient rule. y=u/v dy/dx=(vu'-uv')/v 2 , where u' and v' is the derivative of u and v respectively. Then, apply the rule. u=3x-1, v=2x-1 u'=3...
MM
Answered by Martin M. • Maths tutor
8253 Views

let y=6x^-0.5+2x+1, find dy/dx.

dy/dx = -6(0.5)x^-1.5+2 = -3x^-1.5+2
RL
Answered by Rodger L. • Maths tutor
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Integrate the following fraction w.r.t. x: (sqrt(x^2 + 1)-sqrt(x^2 - 1))/(sqrt(x^4 - 1))

Notice the denominator can be factorised as the difference of two squares. The fraction can then be simplified by cancellation. The resulting fraction(s) can then be solved using the list of integrals in you...
TD
Answered by Tutor80072 D. • Maths tutor
4936 Views

Express (3 - sqrt(5))^2 in the form m + n*sqrt(5), where m and n are integers.

Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)) . Notice that this looks a lot like a factorised quadratic equation , where sqrt(5) can be treated as a variable like x . The...
AP
Answered by Anselmo P. • Maths tutor
9396 Views

(19x - 2)/((5 - x)(1 + 6x)) can be expressed as A/(5-x) + B/(1+6x) where A and B are integers. Find A and B

First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means: (19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction: (19x - 2)/((5 - x)(1 + 6...
TS
Answered by Tarek S. • Maths tutor
3645 Views