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
More Answers:
[next_post_link]