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If n is an integer such that n>1 and f(x)=(sin(n*x))^n, what is f'(x)?

Let us denote sin(nx) = u(x), where u is a function of x. The equation is now therefore f(x) =(u(x))^n. For simplicity, we will write that as f(x) = u^n By the chain rule, we know that f'(x) = df/dx = (df/du...
NT
Answered by Noam T. • Maths tutor
5185 Views

If hydrogen was burnt in a chamber full of oxygen, what would be the effect on the chamber pressure and why?

The equation for the reaction is; 2H 2 +O 2 = 2H 2 O From the equation it can be seen that 2 moles of hydrogen reacts with 1 mole of oxygen to produce 2 moles of water vapour. Since the reaction used more mo...
FO
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What is [(x+1)/(3x^(2)-3)] - [1/(3x+1)] in its simplest form?

First simplify the expression; 3x^(2)-3 to get; [(x+1)/3(x^(2)-1)] - [1/(3x+1)] Using the fact that x^(2)-1 is the difference of two squares, we can simplify it to; [(x+1)/3(x+1)(x-1)] - [1/(3x+1)] which sim...
FO
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x = 2t + 5, y = 3 + 4/t. a) Find dy/dx at (9.5) and b) find y in terms of x.

This is a standard parametric equations question, it is important that the methodology behind answering this question is understood. For part a) we simply use the chain rule (dy/dx = dy/dt X dt/dx) and the r...
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Answered by Jonathan T. • Maths tutor
10714 Views

A student is measuring the acceleration due to gravity, g. They drop a piece of card from rest, from a vertical height of 0.75m above a light gate. The light gate measures the card's speed as it passes to be 3.84 m/s. Calculate an estimate for g.

This question is simply a matter of finding and applying the correct equation of motion. First, draw a diagram - even if the situation in the questions seems really simple, it's always useful to draw a diagr...
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Answered by Philippa M. • Physics tutor
8349 Views