Calculus Examples

Find the Derivative - d/dx f(x)=(4sin(x))/(3+cos(x))
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Differentiate.
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Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Add and .
Step 5
The derivative of with respect to is .
Step 6
Multiply.
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Step 6.1
Multiply by .
Step 6.2
Multiply by .
Step 7
Raise to the power of .
Step 8
Raise to the power of .
Step 9
Use the power rule to combine exponents.
Step 10
Add and .
Step 11
Combine and .
Step 12
Simplify.
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Step 12.1
Apply the distributive property.
Step 12.2
Apply the distributive property.
Step 12.3
Simplify the numerator.
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Step 12.3.1
Simplify each term.
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Step 12.3.1.1
Multiply by .
Step 12.3.1.2
Multiply .
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Step 12.3.1.2.1
Raise to the power of .
Step 12.3.1.2.2
Raise to the power of .
Step 12.3.1.2.3
Use the power rule to combine exponents.
Step 12.3.1.2.4
Add and .
Step 12.3.2
Factor out of .
Step 12.3.3
Factor out of .
Step 12.3.4
Factor out of .
Step 12.3.5
Rearrange terms.
Step 12.3.6
Apply pythagorean identity.
Step 12.3.7
Multiply by .
Step 12.4
Reorder terms.
Step 12.5
Factor out of .
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Step 12.5.1
Factor out of .
Step 12.5.2
Factor out of .
Step 12.5.3
Factor out of .