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Given that y=x/(2x+5) find dy/dx.

Using the quotient rule: Let u=x and v=2x+5 then du/dx= 1 and dv/dx=2 Hence dy/dx=[(2x+5)x1- (2x)]/(2x+5) 2 =5/(2x+5) 2
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Answered by Shayna B. • Maths tutor
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Integrate xsin2x

Integrate by parts: integral = [uv] - ∫u'v dx (u'= derivative of u, v'= derivative of v) u= x u'= 1 v' = sin2x v= -0.5cos2x = -0.5xcosx - ∫-0.5cos2x dx = -0.5xcosx + 0.25sin2x + c
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Answered by Julia E. • Maths tutor
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What is the area bound by the x-axis, the lines x=1 and x=3 and the curve y=3x^(2)-1/x ? Answer in exact form.

Integrate, y= 3x 2 -1/x 1{ 3 3x 2 - 1/x dx = [x-lnx] 3 1 = (3-ln3)-(1-ln1) = 3-ln3-1+0= 2-ln3
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Answered by Escher L. • Maths tutor
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f(x)=x^3 + x^2 -10x +8 show that (x-1) is a factor of f(x), Factorise f(x) fully , sketch the graph of f(x)

f(1)=0 f(x)=(x-1)(x+4)(x-2)
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Answered by Deborah A. • Maths tutor
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Given that y = 4x^3 – 5/(x^2) , x =/= 0, find in its simplest form dy/dx.

We are given: y = 4x^3 – 5/(x^2) To find the dy/dx we are going to use the power rule, from the power rule differentiating x^n gives n*x^n-1, so from our equation differetiating x^3 will give 3x^2, but we ne...
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Answered by Mohamed A. • Maths tutor
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