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givi [52]
3 years ago
10

3√x -2/x^2please show step by step of differentiation before combining the terms. ​

Mathematics
1 answer:
EastWind [94]3 years ago
3 0

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 y = ax^{n}, then \frac{dy}{dx} = nax^{n-1} 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;

y= 3\sqrt{x}  -2/x^2\\y = 3{x}^\frac{1}{2}  - 2x^{-2} \\\\

On differentiating the resulting function;

\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} }

To combine the terms, we will add up by finding their LCM.

\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}}

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