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  • need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 46

need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 46

Answers (1)

Answer: \frac{1}{\sqrt{x^{2}+4 x+1}}

Hint: you must know the rules of solving derivative of logarithm function

Given:   \log \left[x+2+\sqrt{x^{2}+4 x+1}\right]

Solution:

Let  y=\log \left[x+2+\sqrt{x^{2}+4 x+1}\right]

Differentiate both side with respect to x

\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}} \log \left[x+2+\sqrt{x^{2}+4 x+1}\right]

=\frac{1}{\left[x+2+\sqrt{x^{4}+4 x+1}\right]} \times\left[1+0+\frac{1}{2}\left(x^{2}+4 x+1\right)^{\frac{-1}{2}} \frac{\mathrm{d}}{\mathrm{dx}}\left(x^{2}+4 x+1\right)\right]

\Rightarrow \frac{1+\frac{2 x+4}{2\left(\sqrt{x^{2}+4 x+1}\right)}}{\left[x+2+\sqrt{x^{2}+4 x+1}\right]}

=\frac{\sqrt{x^{2}+4 x+1}+x+2}{\left[x+2+\sqrt{x^{2}+4 x+1}\right] \times \sqrt{x^{2}+4 x+1}}

\Rightarrow \frac{1}{\sqrt{x^{2}+4 x+1}}

 

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