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:

$y=\frac{5}{x^2}$

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,

$y^{\prime}=-\frac{10}{x^3}$

The value of dy/dx at x=3:

$\begin{gathered} y^{\prime}=-\frac{10}{3^3} \\ =-\frac{10}{27} \end{gathered}$

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