Calculus Examples

Find dy/dx y=x/(sin(x)+cos(x))
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
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Step 3.1
Differentiate using the Quotient Rule which states that is where and .
Step 3.2
Differentiate.
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Step 3.2.1
Differentiate using the Power Rule which states that is where .
Step 3.2.2
Multiply by .
Step 3.2.3
By the Sum Rule, the derivative of with respect to is .
Step 3.3
The derivative of with respect to is .
Step 3.4
The derivative of with respect to is .
Step 3.5
Simplify.
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Step 3.5.1
Apply the distributive property.
Step 3.5.2
Multiply .
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Step 3.5.2.1
Multiply by .
Step 3.5.2.2
Multiply by .
Step 3.5.3
Reorder terms.
Step 3.5.4
Factor out of .
Step 3.5.5
Factor out of .
Step 3.5.6
Factor out of .
Step 3.5.7
Factor out of .
Step 3.5.8
Factor out of .
Step 3.5.9
Factor out of .
Step 3.5.10
Factor out of .
Step 3.5.11
Rewrite as .
Step 3.5.12
Move the negative in front of the fraction.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .