Calculus Examples

Find the Derivative - d/dx (x/3.5+3.5/x)(x^2+1)
Step 1
Differentiate using the Product 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
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Simplify the expression.
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Step 2.4.1
Add and .
Step 2.4.2
Move to the left of .
Step 2.5
By the Sum Rule, the derivative of with respect to is .
Step 2.6
Since is constant with respect to , the derivative of with respect to is .
Step 2.7
Differentiate using the Power Rule which states that is where .
Step 2.8
Multiply by .
Step 2.9
Since is constant with respect to , the derivative of with respect to is .
Step 2.10
Rewrite as .
Step 2.11
Differentiate using the Power Rule which states that is where .
Step 2.12
Multiply by .
Step 3
Rewrite the expression using the negative exponent rule .
Step 4
Simplify.
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Step 4.1
Apply the distributive property.
Step 4.2
Apply the distributive property.
Step 4.3
Combine terms.
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Step 4.3.1
Combine and .
Step 4.3.2
Combine and .
Step 4.3.3
Raise to the power of .
Step 4.3.4
Raise to the power of .
Step 4.3.5
Use the power rule to combine exponents.
Step 4.3.6
Add and .
Step 4.3.7
Combine and .
Step 4.3.8
Multiply by .
Step 4.3.9
Combine and .
Step 4.3.10
Cancel the common factor of .
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Step 4.3.10.1
Cancel the common factor.
Step 4.3.10.2
Divide by .
Step 4.3.11
Combine and .
Step 4.3.12
Move the negative in front of the fraction.
Step 4.4
Reorder terms.