Calculus Examples

Find the Derivative - d/dx f(x)=3x^4 natural log of x
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Differentiate using the Power Rule.
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Step 4.1
Combine and .
Step 4.2
Cancel the common factor of and .
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Step 4.2.1
Factor out of .
Step 4.2.2
Cancel the common factors.
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Step 4.2.2.1
Raise to the power of .
Step 4.2.2.2
Factor out of .
Step 4.2.2.3
Cancel the common factor.
Step 4.2.2.4
Rewrite the expression.
Step 4.2.2.5
Divide by .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Multiply by .
Step 5.3
Reorder terms.