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In this algebraic problem, we are faced with two unknowns (x's) on both sides of the equation. Remember that what we do to one side, we must also do to the other side. So to tackle this, we will first foc...

let u = x^2              let v  = e^2x

du/dx = 2x             dv/dx = 2e^2x

d/dx = vdu/dx + udv/dx = 2x e^2x + 2x^2e^2x

Therefore

d/dx = ...

We are told that the probability that a randomly chosen teacher is female is 3/5, or 60%.

This means that the overall proportion of female teachers at this school is also 3/5, or 60%.

In tur...

Differentiation is the rate of change of one variable with respect to another at a point in time or space. In other words, this can be described as the slope of a curve, which is how much the curve goes u...

So here we want to eliminate one variable so we are only working with either x or y by themself, so to do this we can rearrange the first equation of x+y=1 to x= 1-y. This new equation can therefore be su...