## d/dx a^u

### To find the derivative of a function involving a variable raised to a function, we can use the chain rule

To find the derivative of a function involving a variable raised to a function, we can use the chain rule. Let’s consider the function f(x) = a^u, where a is a constant and u is a function of x.

Using the chain rule, the derivative of f(x) with respect to x, denoted as df/dx or d/dx(a^u), is calculated as follows:

– First, we differentiate the base function a^u with respect to u, and then multiply it by the derivative of the exponent u with respect to x.

The derivative of a^u with respect to u can be found using the natural logarithm. Specifically, the derivative of a constant raised to a variable with respect to that variable is given by ln(a) * a^u.

The derivative of u with respect to x can be denoted as du/dx.

Putting it all together, we have:

d/dx(a^u) = ln(a) * a^u * du/dx

So, the derivative of a^u with respect to x is ln(a) times a^u times the derivative of u with respect to x.

##### More Answers:

Evaluating the Derivative of e^x | A Step-by-Step GuideThe Chain Rule | Finding the Derivative of e^u with Respect to x

The Chain Rule | Finding the Derivative of f(x) = a^x