derivative of 4x-3/x+1/(x^2) — step-by-step solution

⚠ 4x is read as the product 4*x: for a power, write 4^x

To simplify differentiation, we rewrite

- \frac{3}{x}

-3 x^{-1}

To ease differentiation, the expression

\frac{1}{x^{2}}

is turned into

x^{-2}

Let's perform the differentiation:

\frac{d}{d x} (4 x - 3 x^{-1} + x^{-2})

\frac{d}{d x} (4 x) + \frac{d}{d x} (- 3 x^{-1}) + \frac{d}{d x} (x^{-2})

Apply the differentiation rule:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{(n - 1)}

with f =

x

We differentiate using:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{(n - 1)}

(where f =

x

)

4 - 3 \cdot (-1 \cdot x^{-2}) - 2 x^{-3}

ℹ

-3 \cdot (-1)

3

‖

- 2 x^{-3}

- \frac{2}{x^{3}}

4 + 3 x^{-2} - \frac{2}{x^{3}}

4 + \frac{3}{x^{2}} - \frac{2}{x^{3}}

▶Derivative:

\frac{3}{x^{2}} - \frac{2}{x^{3}} + 4