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Given that f(x) = x^2 (3x - 1)^(1/2) find f'(x)

This is an example of a question using the product rulelet u = x 2 and v = (3x - 1) 1/2 then u' = 2x and v' = 3 X 1/2 (3x - 1) -1/2 using the product rule we get f'(x) = x 2 X 3/2 (3x - 1) -1/2 + (3x - 1) 1/...
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A curve has equation y = x^3 - 48x. The point A on the curve has x coordinate -4. The point B on the curve has x coordinate - 4 + h. Show that that the gradient of the line AB is h^2 - 12h.

First, let's recall the gradient formula:grad = change in y / change in x = y2 -y1 / x2 - x1So let's label point A as x1, and point B as x2, and find the corresponding y1 and y2 using the equation of the cur...
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Answered by Oliver W. • Maths tutor
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Prove by contradiction that 2^(1/3) is an irrational number

Assume 2^(1/3) is rational, so can be written as p/q where p and q are integers with no common factors. p/q = 2^(1/3) (p^3)/(q^3) = 2 p^3 = 2q^3 Hence, p is even. Thus, p can be written as 2r, where r is an ...
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Answered by Oscar R. • Maths tutor
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Whats the Product rule for differentiation and how does it work?

We use the product rule when we want to find the derivative of a product of two functions using their individual derivatives, the product rule can be written out as the following formula: fg'(x) = f(x) g'(x)...
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Answered by Joe M. • Maths tutor
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How to differentiate with respect to x, xsin2x.

There are to parts involving x in this expression, so we need to use the product rule. Let u=x and v=sin2x.So we find u'=1, and v'=2sin2x. Then the formula for the product rule gives us that d/dx(uv)= uv' + ...
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Answered by Emily R. • Maths tutor
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