Answer :
Answer:
Step-by-step explanation:
Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²
In differentiation if [tex]y = ax^{n}[/tex], then [tex]\frac{dy}{dx} = nax^{n-1}[/tex] where n is a constant and dy/dx means we are differentiating the function y with respect to x.
Applying the formula o the question given;
[tex]y= 3\sqrt{x} -2/x^2\\y = 3{x}^\frac{1}{2} - 2x^{-2} \\\\[/tex]
On differentiating the resulting function;
[tex]\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 } - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x} }} + \frac{2}{x^{3} }[/tex]
To combine the terms, we will add up by finding their LCM.
[tex]\frac{dy}{dx} = {\frac{3}{2\sqrt{x} }} + \frac{2}{x^{3} }\\\frac{dy}{dx} = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}[/tex]