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Explain solution RD Sharma class 12 chapter Differentiation exercise 10.5 question 12 maths

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Answer: 10^{10^{x}} \cdot 10^{x} \cdot(\log 10)^{2}

Hint: Diff by \left ( 10 \right )^{10x}

Given: \left ( 10 \right )^{10x}

Solution:  Let y=\left ( 10 \right )^{10x}

Taking log on both sides

        \log y=\log 10^{\left(10^{x}\right)}=10^{x} \log 10
Differentiate w.r.t x,

        \begin{aligned} \frac{1}{y} \frac{d y}{d x}=& \log 10 \frac{d}{d x} 10^{x} \\\\ &=\log 10 \times 10^{x} \cdot \log 10 \end{aligned}

        \begin{aligned} \frac{d y}{d x}=y & \times 10^{x} \times(\log 10)^{2} \\\\ &=10^{10^{x}} \cdot 10^{x}(\log 10)^{2} \end{aligned}

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