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

Use the Binomial Theorem.

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 .

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.

Add and .

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.

Add and .

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.

Add and .

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.

Add and .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Combine the opposite terms in .

Subtract from .

Add and .

Add and .

Add and .

Subtract from .

Add and .

Add and .

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