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  • Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 6

Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 6

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best_answer

Answer:

The answer of the given question will be \frac{1}{9}.

Given:

Let g(x) be the inverse of an invertible function) f(x) which is derivable at x=3. If f (3) =9 and f^{'} (3) =9 find the value of g^{'}(9).

Hint:

\begin{aligned} &g(x) \stackrel{\text { invertible }}{\longrightarrow} f(x) \\\\ &g \circ f(x) \stackrel{\text { invertible }}{\longrightarrow} I(x) \end{aligned}

Solution:  

Differentiating both sides we get,

\begin{aligned} &g \circ f^{\prime}(x)=1 \\\\ &\Rightarrow \frac{d}{d x} g[f(x)]=1 \\\\ &\Rightarrow g^{\prime}[f(x)]=f^{\prime}(x)=1 \end{aligned}

Now x=3

\begin{aligned} &g^{\prime}[f(3)]=\frac{1}{f^{\prime}(3)}[\therefore f(3)=9] \\\\ &\Rightarrow g^{\prime}(9)=\frac{1}{9}\left[f^{\prime}(3)=9\right] \end{aligned}

So the answer will be  \frac{1}{9}

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infoexpert26

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