Calculus Examples

Find the Derivative - d/dx f(x)=(7x)/(4-tan(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
Differentiate.
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Step 3.1
Differentiate using the Power Rule which states that is where .
Step 3.2
Multiply by .
Step 3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Add and .
Step 3.6
Since is constant with respect to , the derivative of with respect to is .
Step 3.7
Multiply.
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Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 4
The derivative of with respect to is .
Step 5
Combine and .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Simplify each term.
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Step 6.2.1
Multiply by .
Step 6.2.2
Multiply by .
Step 6.3
Reorder terms.
Step 6.4
Factor out of .
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Step 6.4.1
Factor out of .
Step 6.4.2
Factor out of .
Step 6.4.3
Factor out of .
Step 6.4.4
Factor out of .
Step 6.4.5
Factor out of .