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Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4

Answer: f'(x) = 15x^2 + 12x -12 This is according to basic rules of differentiation and is a beginner level differentiation question as following:If f(x) = ax^nThen f'(x) = x(nx^n-1)
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Answered by Holly K. • Maths tutor
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Give two reasons why the ratio decidendi of a case is sometimes difficult to determine. Use case law to illustrate your reasons. (4 Marks)

First, judgments are often written in a complex, discursive fashion. It can be difficult to determine the main point that a judge is trying to make. In Woollin, it is unclear from the leading judgement wheth...
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Answered by Tom H. • Law tutor
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Differentiate 5x^3 + 4x^2 + 5x + 9

Differentiate 5x 3 + 4x 2 + 5x + 9The rules from polynomial differentiation: d(ax n ) / dx= a(nx n-1 ) and df/dx + dg/dx = d (f+g) /dx and dn/dx = 0Using these rules in conjunction we get : 5(3x 3-1 ) + 4(2x...
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Answered by Annabelle S. • Maths tutor
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A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).

3x 4/3 -16y 3/4 =32Differentiating implicitly:4x 1/3 -12y -1/4 (dy/dx)=0Simplifying and rearranging:x 1/3 =3y -1/4 (dy/dx)dy/dx=1/3(x 1/3 y 1/4 ) Finding dy/dx using the (x,y) co-ordinates given:dy/dx=1/3(8 ...
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Answered by Ben G. • Maths tutor
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How have the Big Six energy companies benefited from vertical and horizontal integration?

Vertical integration refers to the combination, within a single firm, or two or more stages of production, where each stage was previously undertaken by separate firms. For example, a vertically integrated e...
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Answered by Joshua D. • Economics tutor
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