Answer
The derivative, $f'\left( x \right)$ of the function, $f\left( x \right)=-2{{x}^{2}}+7x-1$ is$-4x+7$.
Work Step by Step
Consider the function,
$f\left( x \right)=-2{{x}^{2}}+7x-1$
Differentiate both sides with respect to x,
$f'\left( x \right)=\frac{d}{dx}\left( -2{{x}^{2}}+7x-1 \right)$
Apply the sum/difference property of differentiation,
$f'\left( x \right)=-\frac{d}{dx}\left( 2{{x}^{2}} \right)+\frac{d}{dx}\left( 7x \right)-\frac{d}{dx}\left( 1 \right)$
Apply the formula $\frac{d}{dx}\left[ c\cdot f\left( x \right) \right]=c\cdot \frac{d}{dx}\left( f\left( x \right) \right)$ for differentiation,
$f'\left( x \right)=-2\frac{d}{dx}\left( {{x}^{2}} \right)+7\frac{d}{dx}\left( x \right)-\frac{d}{dx}\left( 1 \right)$
Apply the power rule for differentiation,
$\begin{align}
& f'\left( x \right)=-2\left( \left( 2 \right)\cdot {{x}^{2-1}} \right)+7\left( \left( 1 \right)\cdot {{x}^{1-1}} \right)-\left( 0 \right) \\
& =-4x+7{{x}^{0}} \\
& =-4x+7
\end{align}$
Hence, the derivative$f'\left( x \right)$ of the function, $f\left( x \right)=-2{{x}^{2}}+7x-1$ is $-4x+7$.
