Calculus Examples

Find the Derivative - d/dx y=x^2sin(x)^4+cos(x)^-2
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Differentiate using the Product Rule which states that is where and .
Step 2.2
Differentiate using the chain rule, which states that is where and .
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Step 2.2.1
To apply the Chain Rule, set as .
Step 2.2.2
Differentiate using the Power Rule which states that is where .
Step 2.2.3
Replace all occurrences of with .
Step 2.3
The derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 3
Evaluate .
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Step 3.1
Differentiate using the chain rule, which states that is where and .
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Step 3.1.1
To apply the Chain Rule, set as .
Step 3.1.2
Differentiate using the Power Rule which states that is where .
Step 3.1.3
Replace all occurrences of with .
Step 3.2
The derivative of with respect to is .
Step 3.3
Multiply by .
Step 4
Simplify.
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Step 4.1
Rewrite the expression using the negative exponent rule .
Step 4.2
Convert from to .
Step 4.3
Reorder terms.
Step 4.4
Simplify each term.
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Step 4.4.1
Rewrite in terms of sines and cosines.
Step 4.4.2
Apply the product rule to .
Step 4.4.3
One to any power is one.
Step 4.4.4
Combine and .
Step 4.4.5
Combine and .
Step 4.5
Simplify each term.
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Step 4.5.1
Factor out of .
Step 4.5.2
Separate fractions.
Step 4.5.3
Convert from to .
Step 4.5.4
Multiply by .
Step 4.5.5
Separate fractions.
Step 4.5.6
Convert from to .
Step 4.5.7
Divide by .