Question

Differentiate a^x with respect to x is​

Answer 1

Answer:

$\frac{\mathrm{d}(a^x)}{\mathrm{d}x}=a^x\ln(a)$

Step-by-step explanation:

Assuming that a is a constant:

let $a^x=y$

Apply the natural logarithm on both sides:

$x \ln a=\ln y$

By doing implicit differentiation:

$\ln a=\frac{1}{y} \cdot \frac{\mathrm{d}y}{\mathrm{d}x}$

$\frac{\mathrm{d}y}{\mathrm{d}x}=y \ln a$

$\frac{\mathrm{d}y}{\mathrm{d}x}=a^x \ln(a)$