Understanding the Quotient Rule and Derivative Simplification

To find the derivative of a quotient of functions

To find the derivative of a product of functions

To solve a differential equation

To integrate a function

Both F and G are denominators

F is the numerator and G is the denominator

Both F and G are numerators

F is the denominator and G is the numerator

-cos(x)

sin(x)

cos(x)

-sin(x)

0

x

1

-1

-cos(x)

-sin(x)

sin(x)

cos(x)

1 + tan^2(x) = sec^2(x)

sin(x) = cos(x)

tan^2(x) + 1 = sec^2(x)

sin^2(x) + cos^2(x) = 1

1 + sin(x)

1 + cos(x)

sin(x) + cos(x)

1 - cos(x)

0

1

2

-1

1 + cos(x)

1 / (1 + cos(x))

cos(x) / (1 + cos(x))

sin(x) / (1 + cos(x))

Because the denominator is zero

Because the numerator is zero

Because the denominator is not a monomial

Because the numerator is not a monomial