Calculus Examples

Find dy/dx y=(1-cos(x))/(sin(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
By the Sum Rule, the derivative of with respect to is .
Step 3.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.3
Add and .
Step 3.2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
The derivative of with respect to is .
Step 3.4
Multiply.
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Step 3.4.1
Multiply by .
Step 3.4.2
Multiply by .
Step 3.5
Raise to the power of .
Step 3.6
Raise to the power of .
Step 3.7
Use the power rule to combine exponents.
Step 3.8
Add and .
Step 3.9
The derivative of with respect to is .
Step 3.10
Simplify.
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Step 3.10.1
Apply the distributive property.
Step 3.10.2
Apply the distributive property.
Step 3.10.3
Simplify the numerator.
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Step 3.10.3.1
Simplify each term.
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Step 3.10.3.1.1
Multiply by .
Step 3.10.3.1.2
Rewrite as .
Step 3.10.3.1.3
Multiply .
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Step 3.10.3.1.3.1
Multiply by .
Step 3.10.3.1.3.2
Multiply by .
Step 3.10.3.1.4
Multiply .
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Step 3.10.3.1.4.1
Raise to the power of .
Step 3.10.3.1.4.2
Raise to the power of .
Step 3.10.3.1.4.3
Use the power rule to combine exponents.
Step 3.10.3.1.4.4
Add and .
Step 3.10.3.2
Move .
Step 3.10.3.3
Apply pythagorean identity.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .