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Find the derivative of the function.$$f(x)=x+2^{x}$$

$$1+2^{x} \ln 2$$

Calculus 1 / AB

Chapter 2

Differentiation

Section 7

Derivatives of Exponential and Logarithmic Functions

Derivatives

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

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Find the derivative with a…

they function after Lex's plus two to the X. Well, how do we take the derivative of a base to the X? Let's see if we could write this as he to the natural log of X with be in front of him. Okay, Let's see now. That's not right. We want to write it into the cool inform either the natural log. And I must break that up because we'll have Peter the X here, then. Probably. Uh huh. My rule with longer them so you can take this part to the front. So it's the product of X times natural log of me. So this function is actually equivalent to this. And if you wanted to take the derivative of either side I've seen through this is gonna be equal. Teoh, let's see. Get anything is just either that anything times the China So we have natural law could be in front. And let's see, we can rearrange that. Put this except here. And then each of the Allen cancel out. So we end up with natural Lockerbie. Time was beating the X. So that's a refresher. On what? These derivatives. I had to get him. So let's take a derivative of a function term. By term, you just get one for the Ekstrom. And here, as we just saw, we got natural log of the base. The natural love too. Times that same function to the X.

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