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

Question

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 (A) - 6 (B) - 12 (C) 6 (D) 12

Tardigrade Admin · Accepted Answer

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

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

- 6

- 12

6

12

$h^{'} (x) = f^{'} [g (x)] \cdot g^{'} (x)$
$h^{'} (- 1) = f^{'} [g (- 1)] g^{'} (- 1) = f^{'} (2) \cdot (3) = (- 4) (3) = - 12$

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

- 6

- 12

6

12

h′(x)=f′[g(x)]⋅g′(x) h′(−1)=f′[g(−1)]g′(−1)=f′(2)⋅(3)=(−4)(3)=−12

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

$h^{'} (x) = f^{'} [g (x)] \cdot g^{'} (x)$
$h^{'} (- 1) = f^{'} [g (- 1)] g^{'} (- 1) = f^{'} (2) \cdot (3) = (- 4) (3) = - 12$