Let f and g be two differentiable functions satisfying g'(5)=34, g(5)=6 and g=f-1. Then f'(6)=

g=f1⇒f(g(x))=x f1(g(x))·g1(x)=1 x=5⇒f1(g(5)) g1(5)=1 f1(6)·34=1 f1(6)=43

Let f and g be two differentiable functions satisfying g'(5)=34, g(5)=6 and g=f-1. Then f'(6)=

g=f1⇒f(g(x))=x f1(g(x))·g1(x)=1 x=5⇒f1(g(5)) g1(5)=1 f1(6)·34=1 f1(6)=43

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Let f and g be two differentiable functions satisfying $g' (5) = \frac{3}{4}$ , g(5)=6 and $g = f^{- 1}$ . Then $f' (6) =$

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$\frac{1}{6}$

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{1}{2}$

answer is D.

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$g = f^{1} \Rightarrow f (g (x)) = x f^{1} (g (x)) \cdot g^{1} (x) = 1 x = 5 \Rightarrow f^{1} (g (5)) g^{1} (5) = 1 f^{1} (6) \cdot \frac{3}{4} = 1 f^{1} (6) = \frac{4}{3}$

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Let f and g be two differentiable functions satisfying g'(5)=34, g(5)=6 and g=f-1. Then f'(6)=

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Let f and g be two differentiable functions satisfying $g' (5) = \frac{3}{4}$ , g(5)=6 and $g = f^{- 1}$ . Then $f' (6) =$