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Find dy/dx of the curve x^3+5xy-2y^2-57=0

3x 2 +5y+5x(dy/dx)-4y(dy/dx)=0 3x 2 +5y=(5x-4y)dy/dx dy/dx=(3x 2 +5y)/(5x-4y)
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Answered by Steven P. • Maths tutor
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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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Sam takes out a £720 loan. Sam will have to pay back the £720 plus an interest rate of 15%. He will have to pay this back in 12 equal monthly instalments. How much must Sam pay monthly?

First, you must find out the total amount to pay back, this amount will be £720 + 15% of £720. To find 15% of £720, we first calculate 720/100 to find 1% and the multiply by 15: 720/100 = 7.2 *15 = 108. Now ...
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Answered by Samuel N. • Maths tutor
4594 Views

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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