Calculus Examples

Find the Derivative - d/dx y = square root of sin( square root of x)
Step 1
Apply basic rules of exponents.
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Step 1.1
Use to rewrite as .
Step 1.2
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
Combine fractions.
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Step 7.1
Move the negative in front of the fraction.
Step 7.2
Combine and .
Step 7.3
Move to the denominator using the negative exponent rule .
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
The derivative of with respect to is .
Step 8.3
Replace all occurrences of with .
Step 9
Differentiate using the Power Rule.
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Step 9.1
Combine and .
Step 9.2
Differentiate using the Power Rule which states that is where .
Step 10
To write as a fraction with a common denominator, multiply by .
Step 11
Combine and .
Step 12
Combine the numerators over the common denominator.
Step 13
Simplify the numerator.
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Step 13.1
Multiply by .
Step 13.2
Subtract from .
Step 14
Move the negative in front of the fraction.
Step 15
Combine and .
Step 16
Multiply by .
Step 17
Multiply.
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Step 17.1
Multiply by .
Step 17.2
Move to the denominator using the negative exponent rule .
Step 18
Simplify.
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Step 18.1
Reorder terms.
Step 18.2
Separate fractions.
Step 18.3
Convert from to .
Step 18.4
Combine and .
Step 18.5
Reorder factors in .