MATHS

Ques.

$If \ x=tlogt \ and \ y=t^{t} \ and \ \frac{\mathrm{d} y}{\mathrm{d} x} - y = m, \ then \ the \ value \ of \ m \ is$

Ans.

$y=t^{t} \\ Taking \ log \ on \ both \ side \\ Therefore, \ logy=tlogt \\ logy=x\\ Differentiating \ the \ above \ w.r.t \ x \\ Therefore,\ \frac{1}{y}\frac{\mathrm{d} y}{\mathrm{d} x}= 1 \\ \frac{\mathrm{d} y}{\mathrm{d} x} = y \\ \frac{\mathrm{d} y}{\mathrm{d} x} - y= 0 \\$