Question

let y=x√x then dy/dx =​

Answer 1

Answer:

As y has repeated infinite powers of x so it can be written as y=x

y

Taking log of both sides, we get logy=y.logx

Differentiating with respect to x

y

1

.

dx

dy

=y.

x

1

+

dx

dy

.logx

∴

dx

dy

=

x

y

.

(1−ylogx)

y

=

x(1−y.logx)

y

2

Answer 2

Step-by-step explanation:

$y = x \sqrt{x}$

$y = x \: \: {x}^{ \frac{1}{2} } \\ y = {x}^{ \frac{3}{2} } \\ differentiating \: with \: respect \: to \: x \\ \dfrac{dy}{dx} = \dfrac{d}{dx} ( {x}^{ \frac{3}{2} } ) \\ = \dfrac{3}{2} \: {x}^{ \frac{1}{2} }$