Calculus Examples

Find the Derivative - d/dx sin(x)cot(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
The derivative of with respect to is .
Step 4
Simplify.
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Step 4.1
Reorder terms.
Step 4.2
Simplify each term.
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Step 4.2.1
Rewrite in terms of sines and cosines.
Step 4.2.2
Apply the product rule to .
Step 4.2.3
Cancel the common factor of .
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Step 4.2.3.1
Move the leading negative in into the numerator.
Step 4.2.3.2
Factor out of .
Step 4.2.3.3
Cancel the common factor.
Step 4.2.3.4
Rewrite the expression.
Step 4.2.4
One to any power is one.
Step 4.2.5
Multiply by .
Step 4.2.6
Move the negative in front of the fraction.
Step 4.2.7
Rewrite in terms of sines and cosines.
Step 4.2.8
Multiply .
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Step 4.2.8.1
Combine and .
Step 4.2.8.2
Raise to the power of .
Step 4.2.8.3
Raise to the power of .
Step 4.2.8.4
Use the power rule to combine exponents.
Step 4.2.8.5
Add and .
Step 4.3
Combine the numerators over the common denominator.
Step 4.4
Rewrite as .
Step 4.5
Factor out of .
Step 4.6
Factor out of .
Step 4.7
Rewrite as .
Step 4.8
Apply pythagorean identity.
Step 4.9
Cancel the common factor of and .
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Step 4.9.1
Factor out of .
Step 4.9.2
Cancel the common factors.
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Step 4.9.2.1
Multiply by .
Step 4.9.2.2
Cancel the common factor.
Step 4.9.2.3
Rewrite the expression.
Step 4.9.2.4
Divide by .