# Calculus / substituing in f(x)+g(x) to find h'(x)

\begin{align} f(x) &=7\\f'(x)&=2\\ g(x) &=2 \\ g'(x)&=-5 \\ h(x) &= f(x) + g(x)\end{align}

Find: $h'(2)$

My attempt was:

$2+7=9$ but it seems to be wrong.

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The question wants the derivative of the sum function $\ h(x) \$ at $\ x = 2 \$ . What is the derivative of $\ f(x) \ + \ g(x) \$ ? –  RecklessReckoner Jun 18 at 23:53
You may be misquoting the problem. For example, if $f(x)$ is identically equal to $2$, then $g'(x)=0$. –  André Nicolas Jun 19 at 0:04
What @AndréNicolas said. The only way I can think of for this problem statement to be valid is if $x$ represents one specific (but unspecified) value at which the given equations are true. But in that case, unless $x = 2$, we have no information at all about $h'$ at $2$. –  David Z Jun 19 at 1:46
It didn't even register on me that the question as stated is inconsistent :/ ... I assumed that if this was a homework problem, it would have been written in the typical fashion, with all given values at the intended value of $\ x \$ (since it was evidently not a function composition problem). –  RecklessReckoner Jun 19 at 3:21

$$h(x)=f(x)+g(x) \Rightarrow h'(x)=f'(x)+g'(x) =2-5=-3 \Rightarrow h'(2)=-3$$
You found $h(2)$. Instead we want to find $h'(2)$. First, take the derivative of $h(x)=f(x)+g(x)$ with respect to $x$ and use the given values above to find $h'(2)$. So $h'(x)=f'(x)+g'(x)$ and we will let $x=2$ to obtain $h'(2)=f'(2)+g'(2)=2+(-5)=-3$. Thus $h'(2)=-3$.