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In the usual notation the value of $\Delta \nabla$ is equal to
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1414 Upvotes
Verified Answer
The correct answer is:
$\Delta-\nabla$
Now, $\Delta \nabla f(x)=\Delta[f(x)-f(x-h)]$
$\therefore$
$$
\begin{aligned}
&=\Delta f(x)-\Delta f(x-h) \\
&=\Delta f(x)-[f(x)-f(x-h)] \\
&=\Delta f(x)-\nabla f(x) \\
\Delta \nabla &=\Delta-\nabla
\end{aligned}
$$
$\therefore$
$$
\begin{aligned}
&=\Delta f(x)-\Delta f(x-h) \\
&=\Delta f(x)-[f(x)-f(x-h)] \\
&=\Delta f(x)-\nabla f(x) \\
\Delta \nabla &=\Delta-\nabla
\end{aligned}
$$
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