Calculus Examples

Find the Derivative - d/dx y=(3 square root of x+2)x^2
Step 1
Use to rewrite as .
Step 2
Differentiate using the Product 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
Move to the left of .
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
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Combine fractions.
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Step 8.1
Move the negative in front of the fraction.
Step 8.2
Combine and .
Step 8.3
Combine and .
Step 8.4
Move to the denominator using the negative exponent rule .
Step 9
Since is constant with respect to , the derivative of with respect to is .
Step 10
Combine fractions.
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Step 10.1
Add and .
Step 10.2
Combine and .
Step 10.3
Simplify the expression.
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Step 10.3.1
Move to the left of .
Step 10.3.2
Move to the numerator using the negative exponent rule .
Step 11
Multiply by by adding the exponents.
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Step 11.1
Move .
Step 11.2
Use the power rule to combine exponents.
Step 11.3
To write as a fraction with a common denominator, multiply by .
Step 11.4
Combine and .
Step 11.5
Combine the numerators over the common denominator.
Step 11.6
Simplify the numerator.
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Step 11.6.1
Multiply by .
Step 11.6.2
Add and .
Step 12
Combine and using a common denominator.
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Step 12.1
Move .
Step 12.2
To write as a fraction with a common denominator, multiply by .
Step 12.3
Combine and .
Step 12.4
Combine the numerators over the common denominator.
Step 13
Multiply by .
Step 14
Simplify.
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Step 14.1
Apply the distributive property.
Step 14.2
Simplify the numerator.
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Step 14.2.1
Simplify each term.
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Step 14.2.1.1
Rewrite using the commutative property of multiplication.
Step 14.2.1.2
Multiply by by adding the exponents.
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Step 14.2.1.2.1
Move .
Step 14.2.1.2.2
Multiply by .
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Step 14.2.1.2.2.1
Raise to the power of .
Step 14.2.1.2.2.2
Use the power rule to combine exponents.
Step 14.2.1.2.3
Write as a fraction with a common denominator.
Step 14.2.1.2.4
Combine the numerators over the common denominator.
Step 14.2.1.2.5
Add and .
Step 14.2.1.3
Multiply by .
Step 14.2.1.4
Multiply by .
Step 14.2.2
Add and .
Step 14.3
Factor out of .
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Step 14.3.1
Factor out of .
Step 14.3.2
Factor out of .
Step 14.3.3
Factor out of .