Calculus Examples

Find the Derivative - d/dx y=sin(tan(7x))
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
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
Simplify the expression.
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Step 3.3.1
Multiply by .
Step 3.3.2
Move to the left of .
Step 4
Simplify.
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Step 4.1
Reorder the factors of .
Step 4.2
Rewrite in terms of sines and cosines.
Step 4.3
Apply the product rule to .
Step 4.4
One to any power is one.
Step 4.5
Combine and .
Step 4.6
Combine and .
Step 4.7
Factor out of .
Step 4.8
Separate fractions.
Step 4.9
Rewrite as a product.
Step 4.10
Write as a fraction with denominator .
Step 4.11
Simplify.
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Step 4.11.1
Divide by .
Step 4.11.2
Convert from to .
Step 4.12
Separate fractions.
Step 4.13
Convert from to .
Step 4.14
Divide by .
Step 4.15
Multiply .
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Step 4.15.1
Raise to the power of .
Step 4.15.2
Raise to the power of .
Step 4.15.3
Use the power rule to combine exponents.
Step 4.15.4
Add and .