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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 th...

Answered by Niall H. • Maths tutor

4343 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/x². Then dy/dx = 0 is equivalent to 9 = 1/x². Taking x² on...

Answered by Martin P. • Maths tutor

4332 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)] / v²We have: u(x) = x⁴ - 1, hence u'(x) = 4x³v(x) = x⁴ + 1, hence v'(x) = 4x³So we have: [(4x...

Answered by Thomas A. • Maths tutor

2960 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 * ...}

Answered by Shafaan J. • Maths tutor

2980 Views

Express x^2 + 10x – 3 in the form (x + p)^2 + q

= We start by halfing the 10 and putting x + 5 in a bracket = (x + 5)^2 = Opening these brackets give us x^2 + 10x + 25 = To make the 25 the same as - 3 we have to minus 28 = Therefore the answer is = (x ...

Answered by Haasan P. • Maths tutor

6781 Views