Calculus Examples

Find the Derivative - d/dx square root of 1-x^2arcsin(x)
Step 1
Use to rewrite as .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Combine and .
Step 5
Differentiate using the chain rule, which states that is where and .
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Step 5.1
To apply the Chain Rule, set as .
Step 5.2
Differentiate using the Power Rule which states that is where .
Step 5.3
Replace all occurrences of with .
Step 6
To write as a fraction with a common denominator, multiply by .
Step 7
Combine and .
Step 8
Combine the numerators over the common denominator.
Step 9
Simplify the numerator.
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Step 9.1
Multiply by .
Step 9.2
Subtract from .
Step 10
Combine fractions.
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Step 10.1
Move the negative in front of the fraction.
Step 10.2
Combine and .
Step 10.3
Move to the denominator using the negative exponent rule .
Step 10.4
Combine and .
Step 11
By the Sum Rule, the derivative of with respect to is .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Add and .
Step 14
Since is constant with respect to , the derivative of with respect to is .
Step 15
Differentiate using the Power Rule which states that is where .
Step 16
Simplify terms.
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Step 16.1
Multiply by .
Step 16.2
Combine and .
Step 16.3
Combine and .
Step 16.4
Factor out of .
Step 17
Cancel the common factors.
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Step 17.1
Factor out of .
Step 17.2
Cancel the common factor.
Step 17.3
Rewrite the expression.
Step 18
Move the negative in front of the fraction.
Step 19
To write as a fraction with a common denominator, multiply by .
Step 20
To write as a fraction with a common denominator, multiply by .
Step 21
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 21.1
Multiply by .
Step 21.2
Use to rewrite as .
Step 21.3
Use the power rule to combine exponents.
Step 21.4
Combine the numerators over the common denominator.
Step 21.5
Add and .
Step 21.6
Cancel the common factor of .
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Step 21.6.1
Cancel the common factor.
Step 21.6.2
Rewrite the expression.
Step 21.7
Multiply by .
Step 21.8
Use to rewrite as .
Step 21.9
Use the power rule to combine exponents.
Step 21.10
Combine the numerators over the common denominator.
Step 21.11
Add and .
Step 21.12
Cancel the common factor of .
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Step 21.12.1
Cancel the common factor.
Step 21.12.2
Rewrite the expression.
Step 22
Combine the numerators over the common denominator.
Step 23
Multiply by by adding the exponents.
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Step 23.1
Use the power rule to combine exponents.
Step 23.2
Combine the numerators over the common denominator.
Step 23.3
Add and .
Step 23.4
Divide by .
Step 24
Simplify .
Step 25
Simplify.
Step 26
Simplify.
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Step 26.1
Simplify the numerator.
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Step 26.1.1
Simplify each term.
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Step 26.1.1.1
Rewrite as .
Step 26.1.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 26.1.2
Reorder factors in .
Step 26.2
Reorder terms.