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differentiate with respect to 'x' : ln(x^2 + 3x + 5)

(2x + 3) / (x 2 + 3x + 5)
AS
Answered by Alec S. • Maths tutor
5363 Views

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

1st Step: Must separate the fractions and simplify: y= (6x 2 -1)/2sqrt(x)= 6x 2 /(2x 1/2 ) - 1/(2x 1/2 ) Cancel 6 with 2 and x 2 with x 1/2 => y= 3x 3/2 - x -1/2 /2 2nd Step: Differentiate: dy/dx= (9/2)x ...
ES
Answered by Elena S. • Maths tutor
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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
4403 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
4485 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.) R 2 = 24 2 + 7 2 R = 25 Therefore 25cos(x + 1.287) (b) minimum value = -1 *...
PB
Answered by Prashan B. • Maths tutor
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