$\dfrac{\sin x-\cos x}{\sin x+\cos x} = \tan\!\left(x-\dfrac{\pi}{4}\right)$

So $f(x)=\tan^{-1}\!\left(\tan\!\left(x-\dfrac{\pi}{4}\right)\right)=x-\dfrac{\pi}{4}$ (within the principal range).

$\dfrac{df}{dx}=1$.

Let $g(x)=x/2$, so $dg/dx=1/2$.

Derivative of $f$ w.r.t. $g$: $\dfrac{df/dx}{dg/dx}=\dfrac{1}{1/2}=\mathbf{2}$

George Eastman introduced roll film and the simple Kodak box camera in 1888. This was revolutionary for several reasons:

• Before Eastman's roll film, photography required heavy glass plates, complex chemical baths, and specialist knowledge — making it impractical for rapid journalistic work
• The Kodak camera was simple enough for anyone to use (“You press the button, we do the rest” was Eastman's slogan), democratising photography
• Roll film was lighter and easier to load than glass plates, making field photography faster and more mobile
• This, combined with the halftone process (1881) and smaller cameras like the 35mm Leica (first marketed 1925), created the conditions for modern photojournalism

The photojournalist tradition — using shocking or revealing images to change public opinion and drive legislation — was enabled directly by these technological advances.