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

Math
Differentiate using the Quotient Rule which states that is where and .
Use the Binomial Theorem.
Simplify each term.
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Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Multiply by .
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
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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.
Tap for more steps…
Apply the product rule to .
Apply the distributive property.
Simplify the numerator.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Move .
Multiply by .
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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.
Tap for more steps…
Move .
Multiply by .
Tap for more steps…
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.
Tap for more steps…
Move .
Multiply by .
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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.
Tap for more steps…
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Tap for more steps…
Apply the power rule and multiply exponents, .
Multiply by .
Apply the product rule to .
Raise to the power of .
Multiply the exponents in .
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Simplify.
Tap for more steps…
Multiply by by adding the exponents.
Tap for more steps…
Move .
Multiply by .
Tap for more steps…
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by by adding the exponents.
Tap for more steps…
Move .
Multiply by .
Tap for more steps…
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by by adding the exponents.
Tap for more steps…
Move .
Multiply by .
Tap for more steps…
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Combine the opposite terms in .
Tap for more steps…
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)


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