# AP Calculus AB : Chain rule and implicit differentiation

## Example Questions

### Example Question #31 : Chain Rule And Implicit Differentiation

Find the derivative of:

Explanation:

On this problem we have to use chain rule, which is:

So in this problem we let

and

.

Since

and

,

we can conclude that

### Example Question #32 : Chain Rule And Implicit Differentiation

Find the derivative of:

Explanation:

On this problem we have to use chain rule, which is:

So in this problem we let

and

.

Since

and

,

we can conclude that

and

### Example Question #33 : Chain Rule And Implicit Differentiation

Find the derivative of:

Explanation:

On this problem we have to use chain rule, which is:

So in this problem we let

and

.

Since

and

,

we can conclude that

### Example Question #31 : Chain Rule And Implicit Differentiation

Find the derivative of:

Explanation:

On this problem we have to use chain rule, which is:

So in this problem we let

and

.

Since

and

,

we can conclude that

### Example Question #35 : Chain Rule And Implicit Differentiation

Find the derivative of:

Explanation:

On this problem we have to use chain rule, which is:

So in this problem we let

and

and

.

Since

and

and

,

we can conclude that

### Example Question #36 : Chain Rule And Implicit Differentiation

Find dy/dx of:

Explanation:

On this problem we have to use chain rule, which is:

So in this problem we let

and

.

Since

and

,

we can conclude that

### Example Question #131 : Computation Of The Derivative

Find the derivative of the following equation:

Explanation:

Because we are differentiating a function within another function, we must use the chain rule, which gives that

.

Using this rule, we see that

,

and therefore, the differentiation of

is

.

### Example Question #431 : Ap Calculus Ab

Find the derivative of the following equation:

Explanation:

Because we are differentiating a function within another function, we must use the chain rule, which states that

.

Looking at our function, we should be able to tell that

and

.

Given this, we can use the chain rule to solve:

.

### Example Question #32 : Chain Rule And Implicit Differentiation

Find the derivative of the following function:

Explanation:

Because we are differentiating a function within another function, we must use the chain rule, which states that

.

By examining the given equation

,

we see that we can find the derivative by pulling out the 5, as it is simply a constant:

.

We can see from this that

and

.

By plugging this information into the chain rule, we find that the derivative is

.

### Example Question #132 : Computation Of The Derivative

Find the derivative of the following equation:

Explanation:

Because we are differentiating a function within another function, we must use the chain rule, which states that

.

from the given equation,

,

we can deduce that in this case,

and .

By plugging this into the chain rule, we find that

.