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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
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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...
JT
Answered by Jonathan T. • Maths tutor
10675 Views

For the curve f(x) = 2x^3 - 54x, find the stationary points and state the nature of these points

Firstly, find the values of x where f'(x) = 0 f'(x) = 6x 2 - 54 6x 2 - 54 = 0 6(x+3)(x-3) = 0 x = 3, y = -108 and x = -3, y = 108 Next, find the values of f''(x) at these points f''(x) = 12x When x = 3, f''(...
RW
Answered by Ruby W. • Maths tutor
4967 Views

Find f'(x) and f''(x) when f(x) = 3x^2 +7x - 3

We know that when f(x) = x^n, f'(x) = nx^n-1 (1) So we apply this to all components of f(x), giving f'(x) = 2(3x) + 7 = 6x +7 to find f''(x), we apply (1) to f'(x). Giving f''(x) = 6
GP
Answered by Georgiana P. • Maths tutor
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