Calculus Examples

Find the Derivative - d/d@VAR h(t) = square root of t(1-t^2)
Step 1
Use to rewrite as .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Differentiate using the Power Rule which states that is where .
Step 3.6
Multiply by .
Step 4
Multiply by by adding the exponents.
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Step 4.1
Move .
Step 4.2
Multiply by .
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Step 4.2.1
Raise to the power of .
Step 4.2.2
Use the power rule to combine exponents.
Step 4.3
Write as a fraction with a common denominator.
Step 4.4
Combine the numerators over the common denominator.
Step 4.5
Add and .
Step 5
Move to the left of .
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
To write as a fraction with a common denominator, multiply by .
Step 8
Combine and .
Step 9
Combine the numerators over the common denominator.
Step 10
Simplify the numerator.
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Step 10.1
Multiply by .
Step 10.2
Subtract from .
Step 11
Move the negative in front of the fraction.
Step 12
Combine and .
Step 13
Move to the denominator using the negative exponent rule .
Step 14
Simplify.
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Step 14.1
Apply the distributive property.
Step 14.2
Combine terms.
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Step 14.2.1
Multiply by .
Step 14.2.2
Combine and .
Step 14.2.3
Move to the numerator using the negative exponent rule .
Step 14.2.4
Multiply by by adding the exponents.
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Step 14.2.4.1
Use the power rule to combine exponents.
Step 14.2.4.2
To write as a fraction with a common denominator, multiply by .
Step 14.2.4.3
Combine and .
Step 14.2.4.4
Combine the numerators over the common denominator.
Step 14.2.4.5
Simplify the numerator.
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Step 14.2.4.5.1
Multiply by .
Step 14.2.4.5.2
Subtract from .
Step 14.2.5
To write as a fraction with a common denominator, multiply by .
Step 14.2.6
Combine and .
Step 14.2.7
Combine the numerators over the common denominator.
Step 14.2.8
Multiply by .
Step 14.2.9
Subtract from .
Step 14.2.10
Move the negative in front of the fraction.
Step 14.3
Reorder terms.