Top answers

differentiate with respect to x: (x^3)(e^x)

because the equation is made up of two functions we can think of them separately when differentiating:f(x)= x^3 f'(x)= 3x^2g(x)= e^x g'(x)= e^xdy/dx= (3x^2 e^x)+ (x^3 e^x)
JS
Answered by Jake S. • Maths tutor
3440 Views

How do you rearrange formula?

First of all we need to identify what it is we're trying to get onto one side of the equation. In this example;y = 2x - 5 we are asked to arrange the formula in terms of x. To do this we need to first get ri...
MT
Answered by Mallory T. • Maths tutor
3795 Views

g(x) = x/(x+3) + 3(2x+1)/(x^2 +x - 6) a)Show that g(x) =(x+1)/(x-2), x>3 b)Find the range of g c)Find the exact value of a for which g(a)=g^(-1)(a).

a) First, we need to factorize (x 2 +x-6) = (x-2)(x+3). Therefore, g(x) = x/(x+3) + 3(2x+1)/(x-2)(x+3) = x(x-2)/(x-2)(x+3) + 3(2x+1)/(x-2)(x+3) = (x 2 -2x + 6x +3)/(x-2)(x+3) = (x 2 +4x+3)/(x-2)(x+3).Now we ...
TM
Answered by Teodora M. • Maths tutor
17474 Views

Find the integral of ((2(7x^(2)-xe^(-2x))-5)/x) . Given that y=27 at x=1, solve the differential equation dy/dx=((2(7x^(2)-xe^(-2x))-5)/-3x).y^(2/3) in terms of y.

Part A)Expand numerator in the integral to get 14x^(2) - 2xe^(-2x)-5Now divide by denominator to get 14x - 2e^(-2x) - 5/xNow integrate to get 7x^(2) + e^(-2x) - 5ln(x)Part B)Get all components of y on the le...
GR
Answered by George R. • Maths tutor
4605 Views

x + y = 11, and x^2 + y^2 = 61, Work out values of y in the form of x

This is a simultaneous equation question, and it is important to read the question and pick out the information we want, and see what we are trying to get to, then work out a pathway on how we will get to it...
VV
Answered by Venkat V. • Maths tutor
5125 Views