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This is an example of a question using the product rulelet u = x² and v = (3x - 1)^1/2then u' = 2x and v' = 3 X 1/2 (3x - 1)^-1/2 using the product rule we get f'(x) = x

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 ...

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 ...

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)

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'...