Question

for the function y=x√x find value of x for which rate of change of y with respect to x is 6

Answer 1

Answer:

$(\frac{dy}{dx})_{x=6}=\frac{3}{2}\sqrt{6}$

Step-by-step explanation:

Formula used:

$\frac{d(x^n)}{dx}=n\:x^{n-1}$

Given:

$y=x\sqrt{x}$

$y=x^{\frac{3}{2}}$

Differentiate with respect to 'x'

$\frac{dy}{dx}=\frac{3}{2}x^{\frac{1}{2}}$

$\frac{dy}{dx}=\frac{3}{2}x^{\frac{1}{2}}$

$\frac{dy}{dx}=\frac{3}{2}\sqrt{x}$

$(\frac{dy}{dx})_{x=6}=\frac{3}{2}\sqrt{6}$

Answer 2

16

Step-by-step explanation:

y=x√x or x^3/2

dy/dx = 6 (given)

dy/dx= 3/2*√x

6=3/2×√x

√x= 4

x=16