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  • Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 24 maths

Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Very short answers question 24 maths

Answers (1)

Answer:

The value of f^{\prime}(1) \text { is } 0

Hint:

Using the chain rule of differentiation.

Given:

f(x)=\log \left\{\frac{u(x)}{v(x)}\right\}, u(1)=v(1) \text { and } u^{\prime}(1)=v^{\prime}(1)=2
Solution:  

Using the chain rule of differentiation

f^{\prime}(x)=\frac{1}{\frac{u(x)}{v(x)}} \cdot \frac{v(x) \cdot u^{\prime}(x)-v^{\prime}(x) \cdot u(x)}{(v(x))^{2}}

f^{\prime}(x)=\frac{v(x) \cdot u^{\prime}(x)-v^{\prime}(x) \cdot u(x)}{u(x) \cdot v(x)}

Putting x=1

f^{\prime}(1)=\frac{v(1) \cdot u^{\prime}(1)-v^{\prime}(1) \cdot u(1)}{u(1) \cdot v(1)}

           =\frac{2 v(1) \cdot-2 u(1)}{u(1) \cdot v(1)}

Since,

\begin{aligned} &u(1)=v(1) \\\\ &2 v(1) \cdot-2 v(1)=0 \\\\ &\text { i.e, } f^{\prime}(1)=0 \end{aligned}

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