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Differentiate 6x^(7/2)-5x^2+7

42x^(5/2)-10x
AH
Answered by Adam H. • Maths tutor
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The curve C has the equation: 16y^3 +9x^2y-54x=0, find the x coordinates of the points on C where dy/dx = 0

C: 16y 3 + 9x 2 y -54x = 0 d/dx(16y 3 ) + d/dx(9x 2 y) + d/dx(-54x) = d/dx(0).............=>48y 2 .dy/dx + 9x 2 .dy/dx + y.18x - 54 = 0 dy/dx(48y 2 +9x 2 ) = 54 - 18xy........................................
EP
Answered by Elliot P. • Maths tutor
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Differentiate y = 3x4-8x3-3

y = 3x 4 -8x 3 -3dy/dx = (3 x 4)x 3 -(8 x 3)x 2 dy/dx = 12x 3 - 24x 2
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Answered by Bhavya G. • Maths tutor
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Evaluate the integral ∫2x√(x^2 +1) dx

The first step is deciding on the method of integration. For this integral it makes the most sense to use substitution.Let u = x 2 + 1Differentiate w.r.t x => du/dx = 2xRearrange for dx=> du/2x = dx Su...
SC
Answered by Sam C. • Maths tutor
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Evaluate the following : ∫ln(x) dx

Integrate by parts:u = ln(x) u' = 1/x v' = 1 v = xBy parts formula: uv - ∫u'v dx Therefore we have: x ln(x) - ∫x 1/x dx = x ln(x) - ∫1 dx = x ln(x) - x (+c)
SM
Answered by Saaqib M. • Maths tutor
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