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If y = e^(ax) Show that x(dy)/(dx) = ...

If ` y = e^(ax)` Show that ` x(dy)/(dx) = y log y . `

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Given, ` y = e^(ax)` …(i)
or ` log y = ax `
Differentiating both sides of eqn. (i) w.r.t.x, we get
` 1/y * (dy)/(dx) = a`
` (dy)/(dx) = ay`
` (dy)/(dx) = ae^(ax)" " [:' y = e^(ax)]`
Multiplying both sides with x, we get
` x (dy)/(dx) = axe^(ax)`
or ` x (dy)/(dx) = y log y `
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