# Calculus 1 : Other Differential Functions

## Example Questions

### Example Question #851 : Other Differential Functions

Find the first derivative of the following function:

Explanation:

To find the first derivative of this particular function is accomplished by applying the power rule which states,

Applying the above rule to the equation,

results in,

### Example Question #852 : Other Differential Functions

Find the first derivative of the function .

Explanation:

To take the derivative, you first use the power rule for differentiating,

,

then you use the chain rule,

.

Also recall the trigonometric rule for differentiating sine,

This produces,

### Example Question #853 : Other Differential Functions

Find the derivative.

Explanation:

Use the quotient rule to find the derivative which states,

.

Given,

the derivatives can be found using the power rule which states,

therefore,

Applying the quotient rule to our function we find the derivative to be as follows.

Simplify.

### Example Question #1041 : Differential Functions

Find the derivative.

Explanation:

Use the power rule to find the derivative.

The power rule states,

.

Applying this rule to the function in the problem results in the following.

### Example Question #1042 : Differential Functions

Find the derivative.

Explanation:

Use the power rule to find the derivative.

The power rule states,

.

Applying this rule to each term of the function results in the following.

Thus, the derivative is 4.

### Example Question #854 : Other Differential Functions

What is the equation for the slope of the tangent line to:

Explanation:

To find the equation for the slope of the tangent line, find the derivative.

To find the derivative, use the power rule.

The power rule states,

.

Applying the power rule to each term in the function results in,

.

Thus, the derivative is .

### Example Question #1041 : Functions

Find the derivative when .

Explanation:

Use the power rule to find the derivative.

The power rule states,

.

Applying the power rule to each term within the function results in the following.

Thus, the derivative is

Now, substitute  for .

### Example Question #1042 : Functions

Find the derivative when .

Explanation:

First, use the power rule to find the derivative.

The power rule states,

.

Applying the power rule to each term in the function results in the following.

Thus, the derivative is .

Now, substitute 2 for x.

.

### Example Question #1043 : Functions

Find the derivative.

Explanation:

Use the product rule to find the derivative.

The product rule states,

.

Given,

and recalling the trigonometry derivative for cosine is,

the derivatives are as follows.

Therefore, using the product rule the derivative becomes,

.

### Example Question #851 : Other Differential Functions

Find the derivative.

Explanation:

Use the power rule to find the derivative.

The power rule states,

.

Applying the power rule to each term in the function results in the following.

.

Thus, the derivative is .