# Calculus 1 : Other Differential Functions

## Example Questions

### Example Question #81 : Other Differential Functions

Find the derivative of the function

Explanation:

To find the derivative of this function we must use the Chain Rule and the Quotient Rule. Applying the Chain Rule to the numerator gives

Now using the Quotient Rule for the function, we find the derivative to be

### Example Question #81 : Other Differential Functions

Find the derivative of

Explanation:

To find the derivative of this function, we must use the Quotient Rule which is

Applying this to the function we are given, with  and  gives us

### Example Question #81 : How To Find Differential Functions

Find the derivative of the following function

Explanation:

To find the derivative of this function we must use the Product Rule and the Quotient Rule. Appling the Product Rule to the numerator of the function gives us

Using this with the Quotient Rule, we find

### Example Question #84 : How To Find Differential Functions

Find the derivative of

Explanation:

To find the derivative of this function we must use the Product Rule and the Chain Rule. If  and  then

Applying these derivatives to the Product Rule gives us

### Example Question #85 : How To Find Differential Functions

Differentiate:

Explanation:

To find the derivative of this function we must use the Product Rule and the Chain Rule. First we set

and

Now differentiating both of these functions gives

Applying this to the Product Rule gives us,

### Example Question #86 : How To Find Differential Functions

Find the derivative of

None of these answers are correct.

Explanation:

To find the derivative of this function we must use the Product Rule and the Chain Rule. If we have

and  then

and

Applying this to the product rule, we find

### Example Question #87 : How To Find Differential Functions

Find the derivative of the function

None of these answers are correct.

Explanation:

To find the derivative of this function, we must use the Product Rule, Quotient Rule, and the Chain Rule. To do this, we first find the derivative of each part.

Using the derivatives of each part we can find the derivative of the numerator using the Product Rule

Finally, putting this into the Quotient Rule gives

### Example Question #88 : How To Find Differential Functions

Differentiate the function

None of these answers are correct.

Explanation:

To differentiate this function we must use the Quotient Rule

Using  and .

The derivative of the function is then

### Example Question #89 : How To Find Differential Functions

Differentiate the following function

None of these answers are correct.

Explanation:

To differentiate this function we must use the Chain Rule. where

Therefore the derivative of the function is

### Example Question #81 : Other Differential Functions

Find the derivative of the function

None of these answers are correct.