Calculus Examples

Find the Derivative - d/dx y=1/( square root of 1-x^2)
Step 1
Apply basic rules of exponents.
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Step 1.1
Use to rewrite as .
Step 1.2
Rewrite as .
Step 1.3
Multiply the exponents in .
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Step 1.3.1
Apply the power rule and multiply exponents, .
Step 1.3.2
Combine and .
Step 1.3.3
Move the negative in front of the fraction.
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
By the Sum Rule, the derivative of with respect to is .
Step 9
Since is constant with respect to , the derivative of with respect to is .
Step 10
Add and .
Step 11
Since is constant with respect to , the derivative of with respect to is .
Step 12
Multiply.
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Step 12.1
Multiply by .
Step 12.2
Multiply by .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Simplify terms.
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Step 14.1
Combine and .
Step 14.2
Combine and .
Step 14.3
Cancel the common factor.
Step 14.4
Rewrite the expression.
Step 14.5
Reorder terms.