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By taking the natural log on both sides we can see that: ln(f(x)) = ln(x)^2 This is a more familiar expression that we know how to differentiate  LHS: f '(x)/f(x), RHS: 2*ln(x)/x By re...

First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...

dy/dx = 24e^6x - sin(x) + 6

For any change that occurs in a chemical system, the equilibrium of that system will shift in order to counteract the change being imposed on that system. For example, if the temperature is increased for ...

The strategy is to consider the horizontal and vertical components of the motion separately, and use the equations of motion in each direction. A few things to remember are: the vertical acceleration is a...