Question

Given the equation of a curve is y=5/x²a)Find the value of dy/dx when x=3

Answer 1

Given equation of a curve is:

`y=(5)/(x^2)`

To find the value of dy/dx at x=3:

Differentiating the equation of curve with respect to x:

`\begin{gathered} y=5x^(-2) \\ y^(\prime)=5(-2x^(-3)) \end{gathered}`

Simplifying,

`y^(\prime)=-(10)/(x^3)`

The value of dy/dx at x=3:

`\begin{gathered} y^(\prime)=-(10)/(3^3) \\ =-(10)/(27) \end{gathered}`

Hence, the value of dy/dx at x=3 is - 10/27.