Calculus Examples

Find the Derivative - d/dx y=x^(4/7)(x+2)
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
Multiply by .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
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Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Move the negative in front of the fraction.
Step 8
Combine and .
Step 9
Move to the denominator using the negative exponent rule .
Step 10
Simplify.
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Step 10.1
Apply the distributive property.
Step 10.2
Combine terms.
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Step 10.2.1
Combine and .
Step 10.2.2
Move to the left of .
Step 10.2.3
Move to the numerator using the negative exponent rule .
Step 10.2.4
Multiply by by adding the exponents.
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Step 10.2.4.1
Move .
Step 10.2.4.2
Multiply by .
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Step 10.2.4.2.1
Raise to the power of .
Step 10.2.4.2.2
Use the power rule to combine exponents.
Step 10.2.4.3
Write as a fraction with a common denominator.
Step 10.2.4.4
Combine the numerators over the common denominator.
Step 10.2.4.5
Add and .
Step 10.2.5
Combine and .
Step 10.2.6
Multiply by .
Step 10.2.7
To write as a fraction with a common denominator, multiply by .
Step 10.2.8
Combine and .
Step 10.2.9
Combine the numerators over the common denominator.
Step 10.2.10
Move to the left of .
Step 10.2.11
Add and .