Calculus Examples

Find the Derivative - d/dt y=(tsin(t))/(1+t)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate using the Product 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
Differentiate using the Power Rule which states that is where .
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 4.6
Differentiate using the Power Rule which states that is where .
Step 4.7
Multiply by .
Step 5
Simplify.
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Step 5.1
Simplify the numerator.
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Step 5.1.1
Simplify each term.
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Step 5.1.1.1
Expand using the FOIL Method.
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Step 5.1.1.1.1
Apply the distributive property.
Step 5.1.1.1.2
Apply the distributive property.
Step 5.1.1.1.3
Apply the distributive property.
Step 5.1.1.2
Simplify each term.
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Step 5.1.1.2.1
Multiply by .
Step 5.1.1.2.2
Multiply by .
Step 5.1.1.2.3
Multiply by by adding the exponents.
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Step 5.1.1.2.3.1
Move .
Step 5.1.1.2.3.2
Multiply by .
Step 5.1.2
Combine the opposite terms in .
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Step 5.1.2.1
Subtract from .
Step 5.1.2.2
Add and .
Step 5.2
Reorder terms.