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Differentiate with respect to x: y=(6x^2-1)/2sqrt(x)

1st Step: Must separate the fractions and simplify:

y= (6x²-1)/2sqrt(x)= 6x²/(2x^1/2) - 1/(2x^1/2)

Cancel 6 with 2 and x

Answered by Elena S. • Maths tutor

8066 Views

i) It is given that f(x)=(-5-33x)/((1+x)(1+5x)), express f(x) in the form A/(1+x) + B/(1+5x) where A,B are integers. ii) hence express the integral of f(x) between x=3 and x=0 in the form (p/q)ln4 where p,q are integers.
i) -7/(1+x) + 2/(1+5x) ii) (-31/5)ln4

DT
Answered by Damon T. • Maths tutor
3747 Views

find the integral of ((3x-2)/(6x^2-8x+3)) with respect to x between x=2 and x=1. (hint use substitution u=denominator)
(ln11)/4

DT
Answered by Damon T. • Maths tutor
3831 Views

1. (a) Express 7cosx - 24sin x in the form R cos (x + a), (b) hence what is the minimum value of this equation
(a) Rcos (x+a) = Rcosxcosa - Rsinxsina

7cosx - 24sinx = Rcosxcosa - Rsinxsina

Rcosa = 7, Rsina = 24

Tan a = 24/7

a = 1.287 (3 S.F.)

R²
PB
Answered by Prashan B. • Maths tutor
12672 Views
Find the normal to the curve y = x^2 at x = 5.
Differentiate the original equation (y = x^2) to find the gradient (m) of the line which is a tangent to the curve.

Dy/dx = 2x

Therefore m = 2

Calculate the negative reciprocal (m2) ...
AS
Answered by Aphisha S. • Maths tutor
3420 Views
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Differentiate with respect to x: y=(6x^2-1)/2sqrt(x)

i) It is given that f(x)=(-5-33x)/((1+x)(1+5x)), express f(x) in the form A/(1+x) + B/(1+5x) where A,B are integers. ii) hence express the integral of f(x) between x=3 and x=0 in the form (p/q)ln4 where p,q are integers.

find the integral of ((3x-2)/(6x^2-8x+3)) with respect to x between x=2 and x=1. (hint use substitution u=denominator)

1. (a) Express 7cosx - 24sin x in the form R cos (x + a), (b) hence what is the minimum value of this equation

Find the normal to the curve y = x^2 at x = 5.

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