How to Find the Derivative of a^x with Respect to x | Step-by-Step Guide and Formula

d/dx a^x

To find the derivative of a^x with respect to x, we can use the following steps:

Step 1: Rewrite the expression
a^x = e^(ln(a^x)) = e^(x * ln(a))

Step 2: Apply the chain rule
Using the chain rule, we can differentiate e^(x * ln(a)) with respect to x

To find the derivative of a^x with respect to x, we can use the following steps:

Step 1: Rewrite the expression
a^x = e^(ln(a^x)) = e^(x * ln(a))

Step 2: Apply the chain rule
Using the chain rule, we can differentiate e^(x * ln(a)) with respect to x. Let’s denote y = x * ln(a).

dy/dx = ln(a)

Step 3: Multiply the result by the derivative of the exponent
Now, we need to multiply the result from step 2 by the derivative of the exponent, which is ln(a).

So, the derivative of a^x with respect to x is dy/dx * ln(a) or ln(a) * a^x.

In summary:
d/dx a^x = ln(a) * a^x

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