Calculus Examples

Find the Derivative - d/dx square root of sin(x)
Step 1
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
The derivative of with respect to is .
Step 9
Combine and .
Step 10
Simplify.
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Step 10.1
Separate fractions.
Step 10.2
Convert from to .
Step 10.3
Combine and .
Step 10.4
Reorder factors in .