### All Calculus 1 Resources

## Example Questions

### Example Question #21 : How To Find Differential Functions

Find

**Possible Answers:**

**Correct answer:**

### Example Question #21 : Other Differential Functions

Differentiate:

with respect to .

**Possible Answers:**

**Correct answer:**

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 #22 : How To Find Differential Functions

Evaluate

**Possible Answers:**

**Correct answer:**

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 #211 : Differential Functions

Integrate

**Possible Answers:**

**Correct answer:**

We can use trigonometric identities to transform integrals that we typically don't know how to integrate.

Thus,

### Example Question #24 : How To Find Differential Functions

Integrate

**Possible Answers:**

**Correct answer:**

We can use trigonometric identities to integrate functions we typically don't know how to integrate.

Thus,

### Example Question #25 : How To Find Differential Functions

Evaluate

**Possible Answers:**

**Correct answer:**

You can transform the limits of integration via u-substitution.

Let

When

When

Thus,

### Example Question #27 : Other Differential Functions

Differentiate the function

**Possible Answers:**

**Correct answer:**

Using the product rule for finding derivatives gives the answer.

### Example Question #212 : Differential Functions

Solve for when

**Possible Answers:**

**Correct answer:**

using the quotient rule:

Foil

combine like-terms to simplify

### Example Question #27 : How To Find Differential Functions

Solve for when

**Possible Answers:**

**Correct answer:**

Using the Product Rule: and chain rule for trignometry functions:

Simplify

### Example Question #28 : How To Find Differential Functions

Find the derivative of

**Possible Answers:**

**Correct answer:**

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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