Calculus Examples

Find the Function f''(x)=12x+sin(x)
Step 1
The function can be found by evaluating the indefinite integral of the derivative .
Step 2
Split the single integral into multiple integrals.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
The integral of with respect to is .
Step 6
Simplify.
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Step 6.1
Combine and .
Step 6.2
Simplify.
Step 7
The function if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.
Step 8
The function can be found by evaluating the indefinite integral of the derivative .
Step 9
Split the single integral into multiple integrals.
Step 10
Since is constant with respect to , move out of the integral.
Step 11
By the Power Rule, the integral of with respect to is .
Step 12
Since is constant with respect to , move out of the integral.
Step 13
The integral of with respect to is .
Step 14
Apply the constant rule.
Step 15
Simplify.
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Step 15.1
Combine and .
Step 15.2
Simplify.
Step 16
The function if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.