Question

How do we do this one there two parts to i t

Answer 1

Given:

`8√(y)=x-5y`

Find: differentiation

Step-by-step explanation: on differentitaion with respect to x

`\begin{gathered} 8√(y)=x-5y \\ (8)/(2)y^{(-1)/(2)}(dy)/(dx)=1-5(dy)/(dx) \\ 4y^{(-1)/(2)}(dy)/(dx)+5(dy)/(dx)=1 \\ (4y^{(-1)/(2)}+5)(dy)/(dx)=1 \\ (dy)/(dx)=\frac{1}{4y^{(-1)/(2)}+5} \end{gathered}`

`\begin{gathered} (-4)/(2)y^{(-3)/(2)}(dy)/(dx)(d^2y)/(dx^2)+5(d^2y)/(dx^2) \\ 0=(-2y^{(-3)/(2)}(dy)/(dx)+5)(d^2y)/(dx^2) \\ (d^2y)/(dx^2)=0 \end{gathered}`

put the value of

`(dy)/(dx)`

we get,

`\begin{gathered} (-2\frac{y^{(-3)/(2)}}{4y^{(-1)/(2)}+5}+5)(d^2y)/(dx^2)=0 \\ (d^2y)/(dx^2)=0 \end{gathered}`