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Let k(x) = f(x)g(x) then k'(x) = limit as h --> 0 of: (h(x+h)-h(x))/h = lim (f(x+h)g(x+h) - f(x)g(x))/h

We can factorise the numerator as:
f(x+h)g(x+h) - f(x)g(x) =f(x+h)g(x+h) -g(x)...

32x + 7

When starting with a fraction with 2 individual components, before any addition, subtraction or simplification can take place, the first step will be making them both having the same denominator. Once you...

Answer: 16x/(x - 2)

Start with the numerator of the first fraction, 16x² + 4x³ , take a factor of 4x² out to get 4x²(4 + x). Then look at the denominator...

Answer: 1/115

The easiest way to solve this problem is to draw part of a tree diagram to see the probabilites of each colour being picked each time Laura pulls a ball out of the bag (a full diagram...