# How do you find #dy/dx# by implicit differentiation given #e^x=lny#?

Use the following differentiation rules:

```
When we use implicit differentiation, we must differentiate with respect to one variable without isolating another.
```

Use the identities above, and implicit differentiation:

Hopefully this helps!

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To find ( \frac{dy}{dx} ) by implicit differentiation given ( e^x = \ln y ), differentiate both sides of the equation with respect to ( x ), then solve for ( \frac{dy}{dx} ).

Differentiate both sides with respect to ( x ):

[ \frac{d}{dx}(e^x) = \frac{d}{dx}(\ln y) ]

[ e^x = \frac{1}{y} \cdot \frac{dy}{dx} ]

Solve for ( \frac{dy}{dx} ):

[ \frac{dy}{dx} = e^x \cdot y ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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