To consider finding the slope, let's discuss the topic of the gradient.

For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:

It is essentially the slope of a multi-dimensional function at any given point

The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.

 at 

x:

y:

The slope is 

To consider finding the slope, let's discuss the topic of the gradient.

For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:

It is essentially the slope of a multi-dimensional function at any given point

Knowledge of the following derivative rules will be necessary:

The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.

 at 

x:

y:

The slope is 

To consider finding the slope, let's discuss the topic of the gradient.

For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:

It is essentially the slope of a multi-dimensional function at any given point

Knowledge of the following derivative rules will be necessary:

Trigonometric derivative: 

Note that u and v may represent large functions, and not just individual variables!

The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.

 at 

x:

y:

The slope is 

To consider finding the slope, let's discuss the topic of the gradient.

For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:

It is essentially the slope of a multi-dimensional function at any given point

Knowledge of the following derivative rules will be necessary:

Derivative of a natural log: 

Trigonometric derivative: 

Note that u may represent large functions, and not just individual variables!

The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.

 at 

x:

y:

The slope is 

Use the power rule to find the derivative.

Remember the power rule is:

Thus, the derivative is 

First, find the derivative using the power rule

Recall the power rule:

Because the derivative is a constant , then the derivative at all points is .

First, find the derivative using the power rule. 

Recall the power rule:

Recall that the derivative of a constant is zero.

The derivative is 

Now, substitute  for .

Uses the product rule to find this derivative.

Recall the product rule:

Use the product rule to find this derivative.

Recall the product rule:

First, find the derivative using the power rule. 

Recall the power rule:

The derivative is .

Now, substitute  for .  The slope of the tangent line at  is .