Differentiate using the Quotient Rule which states that is where and .

The derivative of with respect to is .

By the Sum Rule, the derivative of with respect to is .

Since is constant with respect to , the derivative of with respect to is .

Add and .

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.

Add and .

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.

Add and .

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))