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Let y = 4t/(t^2 + 5). Find dy/dt, writing your answer in it's simplest form, and find all values of t for which dy/dt = 0

We use the quotient rule to find dy/dt. Let u = 4t and v = (t^2 + 5). Then, u' = 4 and v' = 2t. Hence,

dy/dt = u'v - v'u / v²= 4(t^2 + 5) - 4t x 2t / (t^2 + 5)²= 20 - 4t

Answered by Jonathan H. • Maths tutor

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C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.

This question wants us to find: dh/dt. We are given: dV/dt=80π and V=4πh(h+4). The equation to use here is: dh/dt = dh/dV x dV/dt. We kn...

Answered by Suban K. • Maths tutor

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How do you differentiate y=cox(x)/sin(x)?

Since we have to differentiate a fraction, we must use the quotient rule.

The quotient rule: If y = u/v, dy/dx = (vdu/dx - udv/dx)/v²

So we must work out each of the ter...

Answered by Raj C. • Maths tutor

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How do I solve simultaneous equations?

2x + y = 7

3x - y = 8

You cannot find x and y using only one equations, but using both you can! So first you have use algebra to make both equations = y. Try this for the first equation by r...

Answered by Stephanie O. • Maths tutor

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