Question

Let $f$ and $g$ be differentiable functions such that $f\left(3\right)=5,g\left(3\right)=7,f^{\prime }\left(3\right)=13,g^{\prime }\left(3\right)=6,f^{\prime }\left(7\right)=2$, and $g^{\prime }\left(7\right)=0.$ If $h\left(x\right)=\left(fog\right)\left(x\right),$ then $h^{\prime }\left(3\right)=$

• A. $14$
• B. $6$
• C. $12$
• D. $10$

Answer 1

The correct option is C $12$

$f\left(3\right)=5;g\left(3\right)=7;f^{\prime }\left(3\right)=13;g^{\prime }\left(3\right)=6;f^{\prime }\left(7\right)=2$ and $g^{\prime }\left(7\right)=0$

then $h^{\prime }\left(3\right)=$?

$h\left(x\right)=f\left(g\right(x\left)\right)$

$\Rightarrow$ $h^{\prime }\left(x\right)=g^{\prime }\left(x\right).f^{\prime }\left(g\right(x\left)\right)$

$h^{\prime }\left(3\right)=g^{\prime }\left(3\right).f^{\prime }\left(g\right(3\left)\right)$

$=6.f^{\prime }\left(7\right)$

$=6.2$

$=12$