Differentiate 2048?

$\frac{d}{dx} 2x^2$ gives us $4x$ . We then plug in 2048 for $x$ to give us $4(2048) = \boxed{8192}$ .

$\frac{\text{d}}{\text{d}x}f(x)=4x \implies f'(2048)=\boxed{8192}.$

$f(x)\quad =\quad 2{ x }^{ 2 }\\ f'(x)\quad =\quad 4x\\ f'(2048)\quad =\quad 4\quad \times \quad 2048\quad =\quad 8192$

d/dx(2x^2)=4x or the derivative of two times x squared with respect to the variablic input x equals four times x. Henceforth if you plug in the numerical value 2048 into the derivatatic function four times x you will get the value of 8192 as the rate of change at that specific point on the original function.