Evaluate the following derivatives. ddx(x−ln⁡x)

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Evaluate the following derivatives.  ddx(x−ln⁡x)

StrycharzT · Accepted Answer

Step 1  To evaluate the derivatives: ddx(x−ln⁡x)  Solution:  Let y=x−ln⁡x  Taking logarithm on both sides,  ln⁡y=ln⁡x−ln⁡x  ln⁡y=−ln⁡x⋅ln⁡x  ln⁡y=−(ln⁡x)2  Differentiating with respect to x,  1y⋅dydx=−2ln⁡x⋅1x  dydx=−2yln⁡xx  dydx=−2x−ln⁡xln⁡xx  Step 2  Hence, required derivative is dydx=−2x−ln⁡xln⁡xx.

Evaluate the following derivatives. ddx(x−ln⁡x)

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