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Differentiate xe^2

Use product rule. d(uv)/dx = u dv/dx +v du/dxu=x du/dx=1v=e^x dv/dx=e^x
d(xe^x)/dx = xe^x + e^x.1 = e^x(x+1)

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How do I factorise difficult quadratic equations?

A quadratic equation such as 6x² + x - 35 = 0 may appear much harder to solve than a simpler equation which students might be more used to, such as x² + 5x + 6 = 0. In reality, there...

Answered by Freddie G. • Maths tutor

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A stone is thrown upwards with a speed of v metres per second. The stone reaches a maximum height of h metres. h is directly proportional to v^2. When the stone is thrown at 10m/s, max height is 5m. Work out the maximum height reached when v = 24.

(Question 20 in AQA calculator paper from November 2017)This question is really wordy, so the first thing we want to do is condense all the information we are given into more manageable equations! The fir...

Answered by Olivia H. • Maths tutor

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Write x^2+6x-7 in the form (x+a)^2+b where a and b are integers

Complete the square.We want a quadratic we can simplify.Halve the linear term coefficient (6) and square it.Add it to the (x²+6x) term and subtract it from the 7.x²+6x+(6/2)²

Answered by George B. • Maths tutor

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Write as a single fraction in it's simplest form: 2/(y+3)-1/(y-6)

The aim is to find a common denominator, we first therefore cross multiply to get:(2(y-6)-(y+3))/((y+3)(y-6))After expanding the relevant brackets we are left with:(2y-12-y-3)/((y+3)(y-6))Which is simply:...

Answered by James F. • Maths tutor

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