Calculus Examples

Find the Derivative - d/dx (cos(x))/(1-sin(x))
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Multiply.
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Step 3.5.1
Multiply by .
Step 3.5.2
Multiply by .
Step 4
The derivative of with respect to is .
Step 5
Raise to the power of .
Step 6
Raise to the power of .
Step 7
Use the power rule to combine exponents.
Step 8
Add and .
Step 9
Simplify.
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Step 9.1
Apply the distributive property.
Step 9.2
Simplify the numerator.
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Step 9.2.1
Simplify each term.
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Step 9.2.1.1
Multiply by .
Step 9.2.1.2
Multiply .
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Step 9.2.1.2.1
Multiply by .
Step 9.2.1.2.2
Multiply by .
Step 9.2.1.2.3
Raise to the power of .
Step 9.2.1.2.4
Raise to the power of .
Step 9.2.1.2.5
Use the power rule to combine exponents.
Step 9.2.1.2.6
Add and .
Step 9.2.2
Apply pythagorean identity.
Step 9.3
Cancel the common factor of and .
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Step 9.3.1
Reorder terms.
Step 9.3.2
Multiply by .
Step 9.3.3
Cancel the common factors.
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Step 9.3.3.1
Factor out of .
Step 9.3.3.2
Cancel the common factor.
Step 9.3.3.3
Rewrite the expression.