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Differentiate y = (6x-13)^3 with respect to x

We are looking for dy/dx, and in this question, the key rule to remember is the chain rule. Therefore the first thing to do is the easy step, take the 3 down and minus 1 from it, this will give 3(6x-13) 2 . ...
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Answered by Toby S. • Maths tutor
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The quadratic equation 2x^2 + 8x + 1 = 0 has roots a and b. Write down the value of a + b, a*b and a^2 + b^2.

Using Vieta's formulas, which make the correspondence between the sums and products of the roots of a polynomial and its coefficients, we can deduce that a + b = (-8)/2 = -4, a b = 1/2 =0.5 and a^2 + b^2 = (...
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Answered by Andreea I. • Maths tutor
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What is a geometric series?

A geometric series is a series with a constant ratio between successive terms.
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Answered by Ming Fung Y. • Maths tutor
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What is an Inverse function?

An inverse function is a function that "reverses" another function. That is, if f is a function mapping x to y , then the inverse function of f maps y back to x . [1]
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Answered by Ming Fung Y. • Maths tutor
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How do I differentiate f(x) = cos(x)/x?

To answer this question you need to use the quotient rule. dy/dx = (vu' - uv')/v 2 . U = cos(x) which differentiates to -sin(x) so u'= -sin(x) v = x so v' = 1 Therefore, dy/dx = ( -xsin(x) - cos(x) ) / x 2
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Answered by Ewan H. • Maths tutor
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