If y-ln xx- then dydx will be

Given: y=ln nbsp;xx Using division rule for the differentation of the given function, dydx=xddx(lnx) lnxddx(x)x2 dydx=(x×1/x ln x × 1)x^2 dydx=1 lnxx2 H ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Basic Differentiation Rule

If y=ln xx, t...

Question

If $y = \frac{ln x}{x}$ , then $\frac{d y}{d x}$ will be

\frac{1 - ln x}{x}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1 + ln x}{x^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1 - ln x}{x^{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{ln x - 1}{x^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{1 - ln x}{x^{2}}$
$y = \frac{ln x}{x}$
$\frac{d y}{d x} = \frac{x \frac{d}{d x} (ln x) - ln x \frac{d}{d x} (x)}{x^{2}}$
$\frac{d y}{d x} = \frac{1 - ln x}{x^{2}}$

Suggest Corrections

Similar questions

Q. If

y = \frac{ln x}{x}

, then

\frac{d y}{d x}

will be

Q. If

y = x^{x} + \frac{1}{x^{x}}

, then

\frac{d y}{d x} =

Q. If

y = x^{x}

, then find

\frac{d y}{d x}

Q. If

y = (sin x)^{x} + x^{x}

then find

\frac{d y}{d x}

Q. If

y = (ln x)

, then

\frac{d y}{d x}

is equal to:

Join BYJU'S Learning Program

If y=ln xx, then dydx will be

The correct option is C 1−lnxx2y=ln xx dydx=xddx(lnx)−lnxddx(x)x2 dydx=1−lnxx2

If $y = \frac{ln x}{x}$ , then $\frac{d y}{d x}$ will be

The correct option is C $\frac{1 - ln x}{x^{2}}$
$y = \frac{ln x}{x}$
$\frac{d y}{d x} = \frac{x \frac{d}{d x} (ln x) - ln x \frac{d}{d x} (x)}{x^{2}}$
$\frac{d y}{d x} = \frac{1 - ln x}{x^{2}}$