Calculus 1 : Other Differential Functions

Example Questions

Example Question #51 : How To Find Differential Functions

Differentiate the function using known derivatives and applying the product, quotient, and chain rules.

Explanation:

We evaluate this derivative using the chain rule:

,

.

The outside function is:

The inside function is:

Therefore,

, which is our final answer.

Example Question #52 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Explanation:

We use the trig identity .

, which is our final answer.

Example Question #51 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

+ c

+ c

+ c

+ c

+ c

+ c

Explanation:

.

, which is our final answer.

Example Question #52 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Explanation:

.

, which is our final answer.

Example Question #53 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Explanation:

We rewrite the denominator as a negative exponenet in the numerator to make the u-substitution easier to see:

, which is our final answer.

Example Question #56 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Explanation:

, which is our final answer.

Example Question #54 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Explanation:

, which is our final answer.

Example Question #51 : How To Find Differential Functions

Find the derivative of .

Explanation:

The derivative of the difference of two functions is the difference of the derivative of the two functions:

Example Question #1271 : Calculus

Find the derivative of .

Explanation:

We can write the function as

.

Let  .

We then have

.

Example Question #56 : Other Differential Functions

Differentiate the function:

Explanation:

Using the chain rule, , ,

we observe the following:

.

.

, which is our final answer.