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Solve the Simultaneous equations x^2 + y^2 =29, y-x=3.

y=x+3, Substitute into equation 1 : (x^2) + (x+3)^2 = 29Expand the Brackets : (x^2) + (x^2 + 6x + 9) = 29Collect like terms : 2x^2 + 6x - 20 = 0Take out a factor of two : x^2 +3x -10 = 0Factorise : (x-2)(x+5...
TM
Answered by Theo M. • Maths tutor
4056 Views

Find the derivative of the following function with respect to x. y = 5e^x−2xsin(x)

So, what I would be looking for from students who are answering this questions are the application of differentiation techniques that they would have been taught at Year 12. The first step in answering this ...
NH
Answered by Niall H. • Maths tutor
5347 Views

Given y = 9x + 1/x, find the values of x such that dy/dx=0

We are given y as a function of x, let's first compute dy/dx, and then solve the equation dy/dx =0. dy/dx = 9 -1/x 2 . Then dy/dx = 0 is equivalent to 9 = 1/x 2 . Taking x 2 on the LHS and 9 on the RHS we ob...
MP
Answered by Martin P. • Maths tutor
4894 Views

Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.

QUOTIENT RULE: [u(x) / v(x)]' = [u'(x)v(x) - u(x)v'(x)] / v 2 We have: u(x) = x 4 - 1, hence u'(x) = 4x 3 v(x) = x 4 + 1, hence v'(x) = 4x 3 So we have: [(4x 3 ) (x 4 + 1) - (4x 3 ) (x 4 - 1)] / (x 4 + 1) 2 ...
TA
Answered by Thomas A. • Maths tutor
3594 Views

Simplify the following expression: ( (x^5) / (x^2) ) ^ 4

For this question it is key to remember the indices laws. The ones you need to recall for this question are: x a / x b = x a - b , and (x a ) b = x a * b . Using these laws, we can simplify the expression in...
SJ
Answered by Shafaan J. • Maths tutor
3738 Views