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In a question asking us to simplify, we know that our task is to reduce the number of terms presented as far as possible. We should begin inside the brackets by attempting to express both our numbers, 3 and ...

The forces should be resolved in two directions: parallel to the plane, and perpendicular to the plane. Friction will act parallel to the plane (up the slope), and the normal force wil act perpendicular to t...

First substiute sin(theta) = x (This step is not nesecessary but often people find quadratics easier to solve in variables that they usually use). Then due to the fact that the "b" coefficient in t...

Let's first recall the definition of tan(x) = sin(x)/cos(x). Hence, y' = d/dx( sin(x)/cos(x) ). Recall quotient rule for differentiation: ( f(x)/g(x) )' = ( f '(x)^2*g(x) - f(x)*g'(x)^2 ) / g(x)^2 and that d...

We use the quotient rule here which states that if y = f(x)/g(x) then dy/dx = (f'(x)g(x) - g'(x)f(x)) / (g(x)^2). Here f(x) = 4x and g(x) = x^2 + 5, so we have f'(x) = 4 , g'(x) = 2x. This gives us dy/dx = (...