1. Tardigrade
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  4. Assume that h( x )=f( g ( x )), where both f and g are differentiable functions. If g(-1)=2; g prime(-1)=3 and f prime(2)=-4 then the value of h prime(-1) is

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Q. Assume that $h( x )=f( g ( x ))$, where both $f$ and $g$ are differentiable functions. If $g(-1)=2$; $g^{\prime}(-1)=3$ and $f^{\prime}(2)=-4$ then the value of $h^{\prime}(-1)$ is

Continuity and Differentiability

Solution:

$h ' (x) = f ' [g(x)] · g ' (x)$
$h ' (-1) = f ' [g(-1)] g ' (-1) = f ' (2) · (3) = (-4) (3) = - 12$