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Solving harder exponential equations, e.g. 5/[exp(x) + 6exp(-x)] - 1 = 0 . CORE MATHS.

Our example equation is, 5/[exp(x) + 6exp(-x)] - 1 = 0 ,and we wish to solve for x. Note that exp(x) is the same as writing e x I have chosen this one, because it helps illustrate some general good practice ...
MS
Answered by Matthew S. • Maths tutor
4652 Views

How do I differentiate (cosx)/x^2

Label function: y=(cosx)/x 2 Recall quotient rule for functions of form h(x)=f(x)/g(x) given by,h'(x)=(f'(x)g(x)-f(x)g'(x))/(g(x)) 2 Split original equation into f(x)=cosx and g(x)=x 2 Calculate individual d...
CD
Answered by Caelen D. • Maths tutor
17033 Views

You are given the equation of the line y=x^3+x^2-2x. Find the stationary points of the curve and determine the maximum and minimum points and find where it crosses the x-axis and thus sketch the graph

First differentiate the equation to find the equation of the tangents in terms of x. From this set dy/dx=0 because this is the stationary points, from this use the quadratic equation to find the value of x f...
OH
Answered by Oliver H. • Maths tutor
4231 Views

Why does excessive consumption of alcohol lead to negative externalities ?

The private consumer does not consider the effect that their excessive alcohol consumption has on a third party and so the private benefit outweighs the social benefit. There is a welfare loss to society fro...
KE
Answered by Kira E. • Economics tutor
2886 Views

What happened during a sacrifice before the animal was killed? [5]

Before an animal was killed, the sacrificial animal would be driven along a set out route, however only Athenian citizens were allowed onto the Acropolis. A sacrifice was a way of showing respect to the Gods...
AP
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