Calculus Examples

Find the Derivative - d/d@VAR f(x)=5x^(4/3)-2/3x^(3/2)+x^2-3x+1
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
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
Combine and .
Step 2.8
Combine and .
Step 2.9
Multiply by .
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
Differentiate using the Power Rule which states that is where .
Step 3.3
To write as a fraction with a common denominator, multiply by .
Step 3.4
Combine and .
Step 3.5
Combine the numerators over the common denominator.
Step 3.6
Simplify the numerator.
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Step 3.6.1
Multiply by .
Step 3.6.2
Subtract from .
Step 3.7
Combine and .
Step 3.8
Multiply by .
Step 3.9
Multiply by .
Step 3.10
Multiply by .
Step 3.11
Cancel the common factor.
Step 3.12
Divide by .
Step 4
Differentiate using the Power Rule which states that is where .
Step 5
Evaluate .
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Step 5.1
Since is constant with respect to , the derivative of with respect to is .
Step 5.2
Differentiate using the Power Rule which states that is where .
Step 5.3
Multiply by .
Step 6
Since is constant with respect to , the derivative of with respect to is .
Step 7
Simplify.
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Step 7.1
Add and .
Step 7.2
Reorder terms.