# What is the derivative of natural log with exponents?

• mavsqueen06
In summary, the conversation discusses using the chain rule of differentiation to find the derivative of a function with numbers to the "x" power, using the example of f(x)= 7^8^x. The conversation also addresses finding the derivative of a quotient of functions with numbers to the "x" power. The advice given is to use the chain rule and simplify the expression before differentiating.
mavsqueen06
Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=?

Are you talking of:
a) $f(x)=(7^{8})^{x}$
b) $f(x)=7^{8^x}$

mavsqueen06 said:
Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=?

You should find this link useful: "[URL .[/URL]

Last edited by a moderator:
i'm working on the B) one

So, set $$u(x)=8^{x}$$, and use the chain rule of differentiation.

ok, thanks, what about dividing them? do i still use rules of differentiation. for example, 3^x/4^x

Or, use first:
$$\frac{3^{x}}{4^{x}}=(\frac{3}{4})^{x}$$

thanks so much!

## 1. What is the derivative of natural log?

The derivative of natural log, or ln(x), is equal to 1/x.

## 2. How do you find the derivative of natural log?

To find the derivative of natural log, use the formula d/dx ln(x) = 1/x.

## 3. What is the graph of the derivative of natural log?

The graph of the derivative of natural log is a hyperbola with a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

## 4. What is the application of the derivative of natural log?

The derivative of natural log is often used in calculus to solve problems involving exponential functions and growth rates.

## 5. Can the derivative of natural log be negative?

Yes, the derivative of natural log can be negative for values of x less than 1, as the function ln(x) is decreasing for x < 1 and the derivative is equal to 1/x.

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