Let f and g be differentiable functions such that f(3) = 5, g(3) = 7, f’(3) = 13, g’(3) = 6, f'(7) = 2 and g'(7) = 0. If h(x) = (fog) (x), then h'(3) =

Question

Let f and g be differentiable functions such that f(3) = 5, g(3) = 7, f’(3) = 13, g’(3) = 6, f'(7) = 2 and g'(7) = 0. If h(x) = (fog) (x), then h'(3) = (A) 14 (B) 12 (C) 16 (D) 0

Tardigrade Admin · Accepted Answer

h(x)=f(g(x)) h'(x) =f'(g(x)) ⋅ g'(x) h'(3) =f'(g(3)) ⋅ g'(3) [∵ g(3)=7 g'(3)=6] =f'(7) ⋅ 6 =2 × 6=12

Q. Let f and g be differentiable functions such that $f (3) = 5, g (3) = 7, f ’ (3) = 13, g ’ (3) = 6, f^{'} (7) = 2$ and $g^{'} (7) = 0$ . If $h (x) = (f o g) (x)$ , then $h^{'} (3) =$

14

12

16

0

10

$h (x) = f (g (x))$
$h^{'} (x) = f^{'} (g (x)) \cdot g^{'} (x)$
$h^{'} (3) = f^{'} (g (3)) \cdot g^{'} (3)$
$[∵ g (3) = 7 g^{'} (3) = 6]$
$= f^{'} (7) \cdot 6$
$= 2 \times 6 = 12$

Q. Let f and g be differentiable functions such that f(3)=5,g(3)=7,f’(3)=13,g’(3)=6,f′(7)=2 and g′(7)=0. If h(x)=(fog)(x), then h′(3)=

14

12

16

0

10

h(x)=f(g(x)) h′(x)=f′(g(x))⋅g′(x) h′(3)=f′(g(3))⋅g′(3) [∵g(3)=7g′(3)=6] =f′(7)⋅6 =2×6=12

Q. Let f and g be differentiable functions such that $f (3) = 5, g (3) = 7, f ’ (3) = 13, g ’ (3) = 6, f^{'} (7) = 2$ and $g^{'} (7) = 0$ . If $h (x) = (f o g) (x)$ , then $h^{'} (3) =$

$h (x) = f (g (x))$
$h^{'} (x) = f^{'} (g (x)) \cdot g^{'} (x)$
$h^{'} (3) = f^{'} (g (3)) \cdot g^{'} (3)$
$[∵ g (3) = 7 g^{'} (3) = 6]$
$= f^{'} (7) \cdot 6$
$= 2 \times 6 = 12$