# How do you find the derivative of exponential function #y = e^9 ln x#?

Product rule!

So, derivating your function:

Thus,

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To find the derivative of the exponential function ( y = e^{9\ln(x)} ), you can use the chain rule. The derivative is ( \frac{dy}{dx} = e^{9\ln(x)} \cdot \frac{d}{dx}(9\ln(x)) ). Using the chain rule and the derivative of ( \ln(x) ), the derivative simplifies to ( \frac{dy}{dx} = e^{9\ln(x)} \cdot \frac{9}{x} ).

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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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