Devin's Blog

Theorem 2.7 The Product Rule
The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of fg is the first function times the derivative of the second, plus the second function times the derivative of the first.
d/dx [f(x)g(x)] = f(x)g'(x) + g(x)f'(x)

Theorem 2.8 The Quotient Rule
The quotient f/g of two differentiable functions f and g is itself differentiable at all values of x for which g(x) does not equal 0. Moreover, the derivative of f/g is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
d/dx

ex. y = 2x^2 cos x
2x^2-sinx + cosx(4x)
2x(-xsinx + 4cosx)

d/dx [tan x] = sec^2 x
d/dx [sec x] = sec x tan x
d/dx [cot x] = -csc^2 x
d/dx [csc x] = -csc x cot x