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Given y = 2x(x^2 – 1)^5, show that dy/dx = g(x)(x^2 – 1)^4 where g(x) is a function to be determined.

y=2x(x²-1)⁵dy/dx= 2(x²-1)⁵ + 2x*10x(x²-1)⁴dy/dx=(x²-1)⁴(2x²-2+20x²)dy/dx=(x²-1)

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A small stone is projected vertically upwards from a point O with a speed of 19.6m/s. Modelling the stone as a particle moving freely under gravity, find the length of time for which the stone is more than 14.7 m above O

We want to find out the time during which the stone is above a certain point. As this stone is thrown upwards we know that the first time it passes this point it will be on its way up and when it passes t...

Answered by Aaron G. • Maths tutor

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Write √ 45 in the form a √ 5, where a is an integer.

You can separate any surd into factors of the number that is being square rooted, for example when you have a surd such as √ 12 it can be rewritten as √ 2 X √ 6 or √ 3 X √ 4. This is very useful when we w...

Answered by Aaron G. • Maths tutor

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How do you differentiate the curve y = 4x^2 + 7x + 1? And how do you find the gradient of this curve?

To begin with, this question requires you to differentiate the curve y = 4x² + 7x +1 in order to find the gradient. To differentiate this function y in respect to x, we need to reduce the power...

Answered by Katie S. • Maths tutor

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If the hypotenuse of a triangle is 7cm and another side is 4cm, what's the length of the other side? How can I work this out?

The phenomenon you're describing is called 'Pythagoras theorem'. Let's go through it together. You have a right angled triangle, with the hypothesis and one side given. The pythagoras theorem gives you a ...

Answered by Najmeh K. • Maths tutor

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