Calculus Examples

Find the Derivative - d/d@VAR f(x)=(10-cos(x))/(10+sin(x))
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3
The derivative of with respect to is .
Step 4
Differentiate.
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
By the Sum Rule, the derivative of with respect to is .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Add and .
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
Simplify each term.
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Step 6.4.1.1
Multiply .
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Step 6.4.1.1.1
Raise to the power of .
Step 6.4.1.1.2
Raise to the power of .
Step 6.4.1.1.3
Use the power rule to combine exponents.
Step 6.4.1.1.4
Add and .
Step 6.4.1.2
Multiply by .
Step 6.4.1.3
Multiply .
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Step 6.4.1.3.1
Multiply by .
Step 6.4.1.3.2
Multiply by .
Step 6.4.1.4
Multiply .
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Step 6.4.1.4.1
Raise to the power of .
Step 6.4.1.4.2
Raise to the power of .
Step 6.4.1.4.3
Use the power rule to combine exponents.
Step 6.4.1.4.4
Add and .
Step 6.4.2
Move .
Step 6.4.3
Apply pythagorean identity.
Step 6.5
Reorder terms.