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The initial mass is found by putting t=0 into the given equation, so the initial mass is 300g. When the mass has decreased to half its value, M=150g. This gives us 150=300e^-0.05t, so e^-0.05t=1/2. Natura...

They are two rules that are used when differentiating a derivative that has a product with two functions or a term where the one function is divisble by another.For example:f(X) = xe^xorf(x) = (2+4x)/x^2<...

A stationary point is where the gradient of a curve momentarily stops changing.Let's take the example that we want to find the stationary points of the curve y=2x^5 - 5x^2. Find the derivative of the equa...

Part a) requires you to find df/dx for the given function. To do this, we differentiate the function once, which is done by multiplying the power of each 'part' with the part itself and subtracting 1 from...

Consider the positions of each ball as a function of time. Distance (position) is equal to velocity times time. We want 'cos' in the answer, so we'll work with the x axis. For ball P, the position is equa...