Calculus Examples

Find the Derivative - d/dx y = natural log of tan(3x)
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
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Rewrite in terms of sines and cosines.
Step 3
Multiply by the reciprocal of the fraction to divide by .
Step 4
Convert from to .
Step 5
Differentiate using the chain rule, which states that is where and .
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Step 5.1
To apply the Chain Rule, set as .
Step 5.2
The derivative of with respect to is .
Step 5.3
Replace all occurrences of with .
Step 6
Differentiate.
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Step 6.1
Since is constant with respect to , the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Simplify the expression.
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Step 6.3.1
Multiply by .
Step 6.3.2
Move to the left of .
Step 6.3.3
Reorder the factors of .