Calculus Examples

Find the Derivative - d/dx y=(1/x-arcsin(1/x))^4
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Rewrite as .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3
Differentiate using the chain rule, which states that is where and .
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Step 3.1
To apply the Chain Rule, set as .
Step 3.2
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Differentiate using the Power Rule.
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Step 4.1
Rewrite as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Combine fractions.
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Step 4.3.1
Multiply by .
Step 4.3.2
Multiply by .
Step 4.3.3
Combine and .
Step 4.3.4
Move to the denominator using the negative exponent rule .
Step 5
Rewrite the expression using the negative exponent rule .
Step 6
Simplify.
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Step 6.1
Apply the product rule to .
Step 6.2
One to any power is one.