# Find the Derivative Using Quotient Rule – d/dd (df(x))/(dx)=(d(5x^2-7)^3)/(dx)

Differentiate using the Quotient Rule which states that is where and .
Use the Binomial Theorem.
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Raise to the power of .
Multiply by .
Raise to the power of .
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 .
Simplify.
Apply the product rule to .
Apply the distributive property.
Simplify the numerator.
Simplify each term.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Use the Binomial Theorem.
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Raise to the power of .
Multiply by .
Raise to the power of .
Apply the distributive property.
Simplify.
Rewrite using the commutative property of multiplication.
Rewrite using the commutative property of multiplication.
Rewrite using the commutative property of multiplication.
Multiply by .
Simplify each term.
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Simplify.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Combine the opposite terms in .
Subtract from .