Calculus Examples

Find the Derivative - d/dx (sin(3x)^2)/(cos(3x))
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
Move to the left of .
Step 4
Differentiate using the chain rule, which states that is where and .
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Step 4.1
To apply the Chain Rule, set as .
Step 4.2
The derivative of with respect to is .
Step 4.3
Replace all occurrences of with .
Step 5
Raise to the power of .
Step 6
Raise to the power of .
Step 7
Use the power rule to combine exponents.
Step 8
Differentiate.
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Step 8.1
Add and .
Step 8.2
Since is constant with respect to , the derivative of with respect to is .
Step 8.3
Multiply by .
Step 8.4
Differentiate using the Power Rule which states that is where .
Step 8.5
Multiply by .
Step 9
Differentiate using the chain rule, which states that is where and .
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Step 9.1
To apply the Chain Rule, set as .
Step 9.2
The derivative of with respect to is .
Step 9.3
Replace all occurrences of with .
Step 10
Multiply.
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Step 10.1
Multiply by .
Step 10.2
Multiply by .
Step 11
Multiply by by adding the exponents.
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Step 11.1
Move .
Step 11.2
Multiply by .
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Step 11.2.1
Raise to the power of .
Step 11.2.2
Use the power rule to combine exponents.
Step 11.3
Add and .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Simplify the expression.
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Step 14.1
Multiply by .
Step 14.2
Move to the left of .