Calculus Examples

Find the Derivative - d/dt -1/((3+t)^2)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Apply basic rules of exponents.
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Step 2.1
Rewrite as .
Step 2.2
Multiply the exponents in .
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Step 2.2.1
Apply the power rule and multiply exponents, .
Step 2.2.2
Multiply by .
Step 3
Differentiate using the chain rule, which states that is where and .
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Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
Step 4
Differentiate.
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Step 4.1
Multiply by .
Step 4.2
By the Sum Rule, the derivative of with respect to is .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Add and .
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Multiply by .
Step 4.7
Since is constant with respect to , the derivative of with respect to is .
Step 4.8
Simplify the expression.
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Step 4.8.1
Multiply by .
Step 4.8.2
Add and .
Step 5
Simplify.
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Step 5.1
Rewrite the expression using the negative exponent rule .
Step 5.2
Combine and .
Step 5.3
Reorder terms.