Find the derivative of each of these functions. 1. \( f(x)=4 x \) 2. \( y=x^{3} \) 3. \( f(x)=\sqrt{x} \) 4. \( f(x)=3 x^{2}-2 x+5 \) 5. \( y=e^{x}-\sin x \)

The derivative of \( f(x) = 4x \) is simply \( f'(x) = 4 \), as the derivative of a constant multiplied by x is just that constant. For \( y = x^3 \), you apply the power rule, resulting in \( y' = 3x^2 \). Moving on, for \( f(x) = \sqrt{x} \), which can be rewritten as \( x^{1/2} \), the derivative is \( f'(x) = \frac{1}{2}x^{-1/2} \) or alternatively \( \frac{1}{2\sqrt{x}} \). In the case of \( f(x) = 3x^2 - 2x + 5 \), applying the power rule gives \( f'(x) = 6x - 2 \). Lastly, for \( y = e^x - \sin x \), the derivative is \( y' = e^x - \cos x \), as the derivative of \( e^x \) is itself and the derivative of \( \sin x \) is \( \cos x \) (remember to take the negative).