# Find the 2nd Derivative y=csc(x) Find the first derivative.
The derivative of with respect to is .
Reorder the factors of .
Find the second derivative.
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.
The derivative of with respect to is .
Raise to the power of .
Use the power rule to combine exponents.
Simplify.
Apply the distributive property.
Combine terms.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Reorder terms.
Find the third derivative.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
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 .
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.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Rewrite as .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Evaluate .
Differentiate using the chain rule, which states that is where and .
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.
Combine terms.
Reorder the factors of .
Subtract from .
Find the fourth derivative.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
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 .
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.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Rewrite as .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Evaluate .
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 .
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.
Move .
Use the power rule to combine exponents.
Move to the left of .
Rewrite as .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Simplify.
Apply the distributive property.
Apply the distributive property.
Combine terms.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Remove unnecessary parentheses.
Reorder the factors of .     