Calculus Examples

Find the Derivative - d/dq (sin(q)+cos(q))/(sin(q))
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
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
Simplify the numerator.
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Step 6.4.1
Combine the opposite terms in .
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Step 6.4.1.1
Subtract from .
Step 6.4.1.2
Add and .
Step 6.4.2
Simplify each term.
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Step 6.4.2.1
Rewrite using the commutative property of multiplication.
Step 6.4.2.2
Multiply .
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Step 6.4.2.2.1
Raise to the power of .
Step 6.4.2.2.2
Raise to the power of .
Step 6.4.2.2.3
Use the power rule to combine exponents.
Step 6.4.2.2.4
Add and .
Step 6.4.2.3
Multiply .
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Step 6.4.2.3.1
Raise to the power of .
Step 6.4.2.3.2
Raise to the power of .
Step 6.4.2.3.3
Use the power rule to combine exponents.
Step 6.4.2.3.4
Add and .
Step 6.4.3
Factor out of .
Step 6.4.4
Factor out of .
Step 6.4.5
Factor out of .
Step 6.4.6
Apply pythagorean identity.
Step 6.4.7
Multiply by .
Step 6.5
Combine terms.
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Step 6.5.1
Move the negative in front of the fraction.
Step 6.5.2
Convert from to .