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  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 22

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 22

Answers (1)

Answer:  \frac{d y}{d x}=\frac{e^{a x} \sec x \log x}{\sqrt{1-2 x}}\left[a+\tan x+\frac{1}{x \log x}+\frac{1}{1-2 x}\right]

Hint:  Differentiate the equation taking log on both sides

Given:  y=\frac{e^{a x} \sec x \log x}{\sqrt{1-2 x}}

Solution:  

        y=\frac{e^{a x} \sec x \log x}{\sqrt{1-2 x}}

Taking log on both sides,

        \log y=\log \left[\frac{e^{a x} \sec x \log x}{\sqrt{1-2 x}}\right]

                    =\log \left(e^{a x}\right)+\log (\sec x)+\log (\log x)-\log (1-2 x)^{\frac{1}{2}}

        \log y=a x+\log (\sec x)+\log (\log x)-\frac{1}{2} \log (1-2 x)

        \frac{1}{y} \frac{d y}{d x}=a+\frac{\sec x \cdot \tan x}{\sec x}+\frac{1}{\log x} \cdot \frac{1}{x}-\frac{1}{2} \cdot \frac{1(-2)}{(1-2 x)}

        \frac{d y}{d x}=y\left[a+\tan x+\frac{1}{x \log x}+\frac{1}{1-2 x}\right]

        \frac{d y}{d x}=\frac{e^{a x} \sec x \log x}{\sqrt{1-2 x}}\left[a+\tan x+\frac{1}{x \log x}+\frac{1}{1-2 x}\right]

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