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Find dy/dx

Remember quotient rule dy/dx=(u'v-v'u)/v^2

u=4x       u'=4

v=x^2+5         v'=2x

dy/dx=(20-4x^2)/(x^2+5)^2 (simplified)

∫ 5e^3-4x dx=5∫e³ e^-4x dx=5e³ ∫e^-4x d=5e³ [(-1/4)e^-4x ]=-(5/4)e³e^-4x =-(5/4)e^3-4x...

All exponential equations can be reduced to the form m=m₀e^kt, where m₀ is the initial mass. This means for our equation the initial mass is 250g. If the mass has doubled i...

For example, y = 3x³ + 9x² + 2. Determine the stationary points and their nature.

Let's remind ourselves what a stationary point is, and what is meant by the ...

We know that having cos and sin functions in a question is going to cause us problems - we need a single function of x. So, step 1, we need to rewrite sin or cos in terms of the other. How do we choose wh...