# Computing Derivatives

### Topics

## Introduction to Computing Derivatives - At A Glance:

Things to remember for implicit differentiation:

*x'*= 1

- since
*y*is a function of*x*, any derivative involving*y*must use the chain rule

- since
*y*is a function of*x*, taking the derivative of*xy*(or of any other product involving both*x*and*y*) requires the product rule

- since
*y*is a function of*x*, taking the derivative of (or any other quotient involving both*x*and*y*) requires the quotient rule

#### Example 1

If
find |

#### Example 2

Find |

#### Exercise 1

Use implicit differentiation to find *y'*, assuming in the case that *y* is a function of *x*.

*x*^{3}+*y*^{3}= 4*x*

#### Exercise 2

Use implicit differentiation to find *y'*, assuming in the case that *y* is a function of *x*.

*y*= cos(*y*) + 2*x*

#### Exercise 3

implicit differentiation to find *y'*, assuming in the case that *y* is a function of *x*.

- e
^{{y2}}-*x*=*y*

#### Exercise 4

implicit differentiation to find *y'*, assuming in the case that *y* is a function of *x*.

*xy*^{2}+*x*^{3}*y*= 4*x*

#### Exercise 5

implicit differentiation to find *y'*, assuming in the case that *y* is a function of *x*.

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