Question

3 \displaystyle\frac{d}{d x } y +3 \frac{ y }{ x } = 2 { x }^{ 4 } { y }^{ 4 }

Answer 1

Answer:

c)1/4

Explanation:

Given,

\displaystyle\longrightarrow\sf{y=\dfrac{x-4}{2\sqrt x}}⟶y=

2

x

x−4

Then by quotient rule,

\displaystyle\longrightarrow\sf {\dfrac {dy}{dx}=\dfrac {2\sqrt x-2(x-4)\cdot\dfrac {1}{2\sqrt x}}{4x}}⟶

dx

dy

=

4x

2

x

−2(x−4)⋅

2

x

1

dx

dy

=

4x

2

x

−

x

x−4

\displaystyle\longrightarrow\sf {\dfrac {dy}{dx}=\dfrac {(x+4)\sqrt x}{4x^2}}⟶

dx

dy

=

4x

2

(x+4)

x

At \displaystyle\sf {x=4,}

dy

=

4(4)

2

(4+4)

4

\displaystyle\longrightarrow\sf {\underline {\underline {\dfrac {dy}{dx}=\dfrac {1}{4}}}}⟶

dx

dy

=

4

1

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