Calculus Examples

Find the Derivative - d/dx square root of 7x+ square root of 7x+ square root of 7x
Step 1
Simplify with factoring out.
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Step 1.1
Use to rewrite as .
Step 1.2
Factor out of .
Step 1.3
Apply basic rules of exponents.
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Step 1.3.1
Apply the product rule to .
Step 1.3.2
Use to rewrite as .
Step 1.3.3
Use to rewrite as .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
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
Differentiate.
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Step 7.1
Move the negative in front of the fraction.
Step 7.2
Combine fractions.
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Step 7.2.1
Combine and .
Step 7.2.2
Move to the denominator using the negative exponent rule .
Step 7.3
By the Sum Rule, the derivative of with respect to is .
Step 7.4
Since is constant with respect to , the derivative of with respect to is .
Step 7.5
Differentiate using the Power Rule which states that is where .
Step 7.6
Multiply by .
Step 8
Differentiate using the chain rule, which states that is where and .
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Step 8.1
To apply the Chain Rule, set as .
Step 8.2
Differentiate using the Power Rule which states that is where .
Step 8.3
Replace all occurrences of with .
Step 9
To write as a fraction with a common denominator, multiply by .
Step 10
Combine and .
Step 11
Combine the numerators over the common denominator.
Step 12
Simplify the numerator.
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Step 12.1
Multiply by .
Step 12.2
Subtract from .
Step 13
Combine fractions.
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Step 13.1
Move the negative in front of the fraction.
Step 13.2
Combine and .
Step 13.3
Move to the denominator using the negative exponent rule .
Step 14
By the Sum Rule, the derivative of with respect to is .
Step 15
Since is constant with respect to , the derivative of with respect to is .
Step 16
Differentiate using the Power Rule which states that is where .
Step 17
Multiply by .
Step 18
Since is constant with respect to , the derivative of with respect to is .
Step 19
Differentiate using the Power Rule which states that is where .
Step 20
To write as a fraction with a common denominator, multiply by .
Step 21
Combine and .
Step 22
Combine the numerators over the common denominator.
Step 23
Simplify the numerator.
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Step 23.1
Multiply by .
Step 23.2
Subtract from .
Step 24
Move the negative in front of the fraction.
Step 25
Combine and .
Step 26
Combine and .
Step 27
Simplify the expression.
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Step 27.1
Move to the denominator using the negative exponent rule .
Step 27.2
Reorder the factors of .