Question

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

Answer 1

Step-by-step explanation:

dy

)

x=6

=

2

3

6

Step-by-step explanation:

Formula used:

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

dx

d(x

n

)

=nx

n−1

Given:

y=x\sqrt{x}y=x

x

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

2

3

Differentiate with respect to 'x'

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

dx

dy

=

2

3

x

2

1

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

dx

dy

=

2

3

x

2

1

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

dx

dy

=

2

3

x

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

dx

dy

)

x=6

=

2

3

6