Calculus Examples

Find the Derivative - d/dx y=(sin(3x^2))/( log of 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
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate.
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
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
Combine and .
Step 6
Differentiate using the chain rule, which states that is where and .
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Step 6.1
To apply the Chain Rule, set as .
Step 6.2
The derivative of with respect to is .
Step 6.3
Replace all occurrences of with .
Step 7
Differentiate.
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Step 7.1
Multiply by .
Step 7.2
Combine fractions.
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Step 7.2.1
Multiply by .
Step 7.2.2
Combine and .
Step 7.3
Since is constant with respect to , the derivative of with respect to is .
Step 7.4
Combine and .
Step 7.5
Differentiate using the Power Rule which states that is where .
Step 7.6
Multiply by .
Step 8
Multiply by .
Step 9
Combine.
Step 10
Apply the distributive property.
Step 11
Cancel the common factor of .
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Step 11.1
Cancel the common factor.
Step 11.2
Rewrite the expression.
Step 12
Simplify.
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Step 12.1
Simplify the numerator.
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Step 12.1.1
Simplify each term.
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Step 12.1.1.1
Simplify by moving inside the logarithm.
Step 12.1.1.2
Raise to the power of .
Step 12.1.2
Reorder factors in .
Step 12.2
Reorder terms.