Calculus Examples

Find the Derivative - d/dx y=sec( square root of x)^2
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
Differentiate using the chain rule, which states that is where and .
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Step 3.1
To apply the Chain Rule, set as .
Step 3.2
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Raise to the power of .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Add and .
Step 8
Differentiate using the Power Rule which states that is where .
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
Move the negative in front of the fraction.
Step 14
Combine and .
Step 15
Combine and .
Step 16
Combine and .
Step 17
Combine and .
Step 18
Simplify the expression.
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Step 18.1
Move to the left of .
Step 18.2
Move to the denominator using the negative exponent rule .
Step 19
Cancel the common factor.
Step 20
Rewrite the expression.