Derivative of a logarithmic function with $\frac{C}{x}$

Question

The function is

$$G(x)=4^{\frac{C}{x}}$$ I have $u=\frac{C}{x}$, then I calculate $$\frac{d}{du}4^u=u(4)^{u-1}$$ But does $$\frac{d}{dx}\frac{C}{x}=C$$ because I don't know if $C$ is a constant or a independent variable.

Answer 1

HINT

if $f(x) = a^x$ you can write

$$ f(x) = e^{\ln a^x} = e^{x \ln a} $$

So the derivative is

$$ \frac{{\rm d}f}{{\rm d}x} = (\ln a )e^{x\ln a} = a^x \ln a $$