Differentiate the following w.r.t. $x$ .
$5 x^{3 / 2}$ .

\frac{3}{2} x^{1 / 2}

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

\frac{5}{2} x^{1 / 2}

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

\frac{15}{2} x^{1 / 2}

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

\frac{15}{2} x^{3 / 2}

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

Open in App

Solution

The correct option is C $\frac{15}{2} x^{1 / 2}$
$\frac{d}{d x} 5 x^{3 / 2}$
$= \frac{3}{2} 5 x^{\frac{3}{2} - \frac{1}{2}} . \frac{d}{d x} (x)$
$= \frac{3}{2} \times 5 x^{1 / 2} .1$
$= \frac{15}{2} x^{1 / 2}$

Suggest Corrections

Similar questions

The anti derivative of equals

(A) (B)

\int \frac{x^{3 / 2} + x^{5 / 2} + x}{x^{2} + 2 x^{1 / 2} + x + 1} d x

\tan^{- 1} (\frac{2 x}{1 - x^{2}})

\cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}), if 0 < x < 1

Consider the system of equations
$x_{1} + 2 x_{2} + 3 x_{3} = 1$
$x_{2} + 2 x_{3} + 3 x_{1} = 2$
$x_{3} + 2 x_{1} + 3 x_{2} = 3$
then

A. $x_{1} = \frac{2}{3}$

B. $x_{1} + x_{2} = \frac{4}{3}$

C. $x_{3} = - \frac{1}{3}$

D. $x_{1} - x_{2} = \frac{1}{3}$

Join BYJU'S Learning Program