Calculus Examples

Find the Derivative - d/dt fourth root of t+6csc(t)
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Use to rewrite as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
To write as a fraction with a common denominator, multiply by .
Step 2.4
Combine and .
Step 2.5
Combine the numerators over the common denominator.
Step 2.6
Simplify the numerator.
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Step 2.6.1
Multiply by .
Step 2.6.2
Subtract from .
Step 2.7
Move the negative in front of the fraction.
Step 3
Evaluate .
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
The derivative of with respect to is .
Step 3.3
Multiply by .
Step 4
Simplify.
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Step 4.1
Rewrite the expression using the negative exponent rule .
Step 4.2
Multiply by .
Step 4.3
Reorder terms.