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Example Questions
Example Question #21 : How To Find Differential Functions
Find
Example Question #22 : How To Find Differential Functions
Differentiate:
with respect to .
Apply the chain rule: differentiate the "outside" function first. Let .
Differentiate the "inside" function next.
Multiply these two functions to find the derivative of the original function.
Example Question #23 : How To Find Differential Functions
Evaluate
To integrate the function, integrate each term of the function. e.g., integrate by increasing the exponent by 1 integer and dividing the term by this new integer: .
Do this for the rest to get .
But remember that every integration requires an arbitrary constant, . Thus, the integral of the function is
Example Question #24 : How To Find Differential Functions
Integrate
We can use trigonometric identities to transform integrals that we typically don't know how to integrate.
Thus,
Example Question #212 : Functions
Integrate
We can use trigonometric identities to integrate functions we typically don't know how to integrate.
Thus,
Example Question #26 : How To Find Differential Functions
Evaluate
You can transform the limits of integration via u-substitution.
Let
When
When
Thus,
Example Question #213 : Functions
Differentiate the function
Using the product rule for finding derivatives gives the answer.
Example Question #25 : How To Find Differential Functions
Solve for when
using the quotient rule:
Foil
combine like-terms to simplify
Example Question #26 : How To Find Differential Functions
Solve for when
Using the Product Rule: and chain rule for trignometry functions:
Simplify
Example Question #216 : Functions
Find the derivative of
The quantity square root of raised to the third is the same as . Using the chain rule and power rule, the answer can be found.
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