List of top Mathematics & Statistics Questions on Switching Circuits

Let \( f(1) = 3 \), \( f'(1) = -\frac{1}{3} \), \( g(1) = -4 \), and \( g'(1) = -\frac{8}{3} \). The derivative of \( \sqrt{[f(x)]^2 + [g(x)]^2} \) w.r.t. \( x \) at \( x = 1 \) is ........

Express the following switching circuit in the symbolic form of logic. Construct the switching table and interpret it. \includegraphics[width=0.5\linewidth]{01.jpeg}

If \( x = f(t) \) and \( y = g(t) \) are differentiable functions of \( t \) so that \( y \) is a function of \( x \) and if \( \frac{dx}{dt} \neq 0 \), then prove that \[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}. \] Hence, find the derivative of \( 7^x \) with respect to \( x^7 \).