Calculus Examples

Find the Derivative - d/dx y=(sin(x)+cos(x))sec(x)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
By the Sum Rule, the derivative of with respect to is .
Step 4
The derivative of with respect to is .
Step 5
The derivative of with respect to is .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Apply the distributive property.
Step 6.4
Reorder terms.
Step 6.5
Simplify each term.
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Step 6.5.1
Rewrite in terms of sines and cosines.
Step 6.5.2
Combine and .
Step 6.5.3
Rewrite in terms of sines and cosines.
Step 6.5.4
Multiply .
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Step 6.5.4.1
Multiply by .
Step 6.5.4.2
Raise to the power of .
Step 6.5.4.3
Raise to the power of .
Step 6.5.4.4
Use the power rule to combine exponents.
Step 6.5.4.5
Add and .
Step 6.5.4.6
Raise to the power of .
Step 6.5.4.7
Raise to the power of .
Step 6.5.4.8
Use the power rule to combine exponents.
Step 6.5.4.9
Add and .
Step 6.5.5
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 6.5.5.1
Reorder and .
Step 6.5.5.2
Rewrite in terms of sines and cosines.
Step 6.5.5.3
Cancel the common factors.
Step 6.5.6
Multiply by .
Step 6.5.7
Rewrite in terms of sines and cosines.
Step 6.5.8
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 6.5.8.1
Reorder and .
Step 6.5.8.2
Rewrite in terms of sines and cosines.
Step 6.5.8.3
Cancel the common factors.
Step 6.5.9
Rewrite in terms of sines and cosines.
Step 6.5.10
Combine and .
Step 6.6
Combine the opposite terms in .
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Step 6.6.1
Subtract from .
Step 6.6.2
Add and .
Step 6.7
Convert from to .
Step 6.8
Apply pythagorean identity.