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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 / v 2 = 4(t^2 + 5) - 4t x 2t / (t^2 + 5) 2 = 20 - 4t 2 / (t^2 + 5) 2 . Now, we need to...
JH
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 know dV/dt, but still need to find dh/dV . For this, we can use the rec...
SK
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 = (v du/dx - u dv/dx)/v 2 So we must work out each of the terms u, v, du/dx and dv/dx from the q...
RC
Answered by Raj C. • Maths tutor
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5Sin[x]-4=2Cos[2x]

x = 0.848,2.29
MM
Answered by Mostafa M. • Maths tutor
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What is differentiation and how is it used?

Differentiation is a branch of calculus mathematics used to determine the rate of change between certain variables. For example if an object changes its distance x over a certain time interval t, we can use ...
AB
Answered by Alper B. • Maths tutor
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