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

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

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Add and .

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

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Add and .

Apply the distributive property.

Apply the distributive property.

Simplify the numerator.

Simplify each term.

Expand by multiplying each term in the first expression by each term in the second expression.

Simplify each term.

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Add and .

Add and .

Add and .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Subtract from .

Subtract from .

Subtract from .

Add and .

Subtract from .

Find the Derivative Using Quotient Rule – d/dm (2m^4+21m^3+35m^2-37m+45)/(2m+7)