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Q.(d) Find the differential coefficient of x⋅log⁡exx \cdot \log_e x.

ChseodishaCHSE Odisha Plus Two (Class 12) Commerce Board 2019Subjective· 2mImportance★★★★★est
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The differential coefficient is log⁡ex+1\log_e x + 1.

The expression x⋅log⁡exx\cdot\log_e x is a product of two functions, so apply the product rule ddx(uv)=udvdx+vdudx\dfrac{d}{dx}(uv) = u\dfrac{dv}{dx} + v\dfrac{du}{dx} with u=xu = x and v=log⁡exv = \log_e x.

Using ddx(x)=1\dfrac{d}{dx}(x) = 1 and ddx(log⁡ex)=1x\dfrac{d}{dx}(\log_e x) = \dfrac{1}{x}: …

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