# Find the Derivative – d/dt (sin(t))/(1-cos(t))

Differentiate using the Quotient Rule which states that is where and .
The derivative of with respect to is .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Multiply.
Multiply by .
Multiply by .
The derivative of with respect to is .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Simplify.
Apply the distributive property.
Simplify the numerator.
Simplify each term.
Multiply by .
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Factor out of .
Factor out of .
Factor out of .
Apply pythagorean identity.
Multiply by .
Combine terms.
Cancel the common factor of and .
Factor out of .
Rewrite as .
Factor out of .
Reorder terms.
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Find the Derivative – d/dt (sin(t))/(1-cos(t))