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What is the chain rule, product rule and quotient rule and when do I use them?

The chain rule, product rule and quotient rule are all 3 methods of differentiating complex functions. Chain rule The chain rule is as follows: (dy/dx) = (dy/dz).(dz/dx) or D{f(g(x))}/dx = f'(g(x)).g'(x) The...
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Answered by Hakeem K. • Maths tutor
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How do I calculate the rate of change of something for which I don't have an equation?

This kind of question is an application of differentiation. If t represents time, any derivative with respect to t is a rate of change. For example, if h represents the depth of water in a cubicle container,...
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Answered by Sam E. • Maths tutor
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How can we determine stationary points by completing the square?

Suppose we have completed the square on y=ax^2+bx+c and attained y=a(x+p)^2+q, where a,b,c,p,q are real numbers with 'a' not equal to zero and p,q can be expressed in terms of a,b,c. For a>0 we have a min...
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Answered by Hayk Y. • Maths tutor
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How do you derive the quadratic formula?

The quadratic formula is the formula that solves any quadratic equation. So, keeping things general, let's begin with a completely general quadratic equation: ax 2 +bx+c=0 This is completely general because ...
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Answered by Aneesh N. • Maths tutor
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How do I expand a factorised equation?

Firstly put the equation into the the form (x+a)(x+b) this will make things easier later on. Therefore, an equation such as (x+1) 2 would become (x+1)(x+1) Next expand the brackets. To do this simply multipl...
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Answered by Emily G. • Maths tutor
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