Calculus Examples

Find the Derivative - d/dx y=x^5 natural log of x-1/3x^3
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
Tap for more steps...
Step 2.1
Differentiate using the Product Rule which states that is where and .
Step 2.2
The derivative of with respect to is .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Combine and .
Step 2.5
Cancel the common factor of and .
Tap for more steps...
Step 2.5.1
Factor out of .
Step 2.5.2
Cancel the common factors.
Tap for more steps...
Step 2.5.2.1
Raise to the power of .
Step 2.5.2.2
Factor out of .
Step 2.5.2.3
Cancel the common factor.
Step 2.5.2.4
Rewrite the expression.
Step 2.5.2.5
Divide by .
Step 3
Evaluate .
Tap for more steps...
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
Multiply by .
Step 3.4
Combine and .
Step 3.5
Combine and .
Step 3.6
Cancel the common factor of and .
Tap for more steps...
Step 3.6.1
Factor out of .
Step 3.6.2
Cancel the common factors.
Tap for more steps...
Step 3.6.2.1
Factor out of .
Step 3.6.2.2
Cancel the common factor.
Step 3.6.2.3
Rewrite the expression.
Step 3.6.2.4
Divide by .
Step 4
Reorder terms.