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  • Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 35

Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 35

Answers (1)

Answer:  \frac{d y}{d x}=\cos \left(x^{x}\right) \cdot x^{x}(1+\log x)

Hint: Differentiate the equation by taking log on both the sides

Given: y=\sin (x)^{x}

Solution:  

Let take u=(x)^{x}

        \begin{aligned} &y=\sin u \\\\ &\frac{d y}{d x}=\cos u \cdot \frac{d u}{d x} \end{aligned}

        \frac{d}{d x}(\log u)=\frac{d}{d x}(x \log x)

        \begin{aligned} &\frac{1}{u} \cdot \frac{d u}{d x}=\log x \cdot \frac{d x}{d x}+x \cdot \frac{d}{d x}(\log x) \\\\ &\frac{d u}{d x}=u\left[\log x+x \cdot \frac{1}{x}\right] \\\\ &\frac{d u}{d x}=x^{x}[\log x+1] \end{aligned}

Put the value of  du/dx we get

        \frac{d y}{d x}=\cos \left(x^{x}\right) \cdot x^{x} \cdot \log (x+1)

 

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