If $f(x)=4h(x)+6x$, find $v(2)$

Key takeaway: This is a calculus chain-rule style evaluation problem. The key is to use the derivative information shown in the prompt and plug in the requested input value carefully.

Step 1: Identify the relevant derivative idea

The prompt shows the derivative expression

$h'(x)+4h(x)+6$

and then evaluates it at $x=2$.

Step 2: Substitute $x=2$

a direct substitution gives

$\frac{4}{4}+6=8$

Step 3: State the result

So the requested value is

$8$

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Pitfalls the pros know 👇 A common mistake is mixing up the function names and reading $f(x)$, $h(x)$, and $v(2)$ as if they were all the same object. Always check which quantity the question actually asks for before substituting.

What if the problem changes? If the problem had asked for the derivative at a different input, the same procedure would apply: identify the derivative formula first, then substitute the new $x$-value into that expression.

Tags: derivative evaluation, chain rule, substitution