Find the 2nd Derivative y=csc(x)

Math
Find the first derivative.
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The derivative of with respect to is .
Reorder the factors of .
Find the second derivative.
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
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 .
The derivative of with respect to is .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify.
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Apply the distributive property.
Combine terms.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Reorder terms.
Find the third derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
The derivative of with respect to is .
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 .
Move to the left of .
Rewrite as .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Evaluate .
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Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
The derivative of with respect to is .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Combine terms.
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Reorder the factors of .
Subtract from .
Find the fourth derivative.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Differentiate using the chain rule, which states that is where and .
Tap for more steps…
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
The derivative of with respect to is .
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 .
Move to the left of .
Rewrite as .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Differentiate using the chain rule, which states that is where and .
Tap for more steps…
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
The derivative of with respect to is .
Multiply by by adding the exponents.
Tap for more steps…
Move .
Use the power rule to combine exponents.
Add and .
Move to the left of .
Rewrite as .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify.
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Apply the distributive property.
Apply the distributive property.
Combine terms.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Remove unnecessary parentheses.
Reorder the factors of .
Add and .
Find the 2nd Derivative y=csc(x)

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