What is the derivative of sqrt(x)-3x^2+8x^{-2} ?

The derivative of sqrt(x)-3x^2+8x^{-2} is (x^{5/2}-32-12x^4)/(2x^{5/2)sqrt(x)}

What is the first derivative of sqrt(x)-3x^2+8x^{-2} ?

The first derivative of sqrt(x)-3x^2+8x^{-2} is (x^{5/2}-32-12x^4)/(2x^{5/2)sqrt(x)}

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\frac{d}{d x} (x - 3 x^{2} + 8 x^{- 2})

\frac{x ^{\frac{5}{2}} - 32 - 12 x ^{4}}{2 x ^{\frac{5}{2}} x}

Solution steps

\frac{d}{d x} (x - 3 x^{2} + 8 x^{- 2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x) - \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (8 x^{- 2})

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (8 x^{- 2}) = - \frac{16}{x ^{3}}

= \frac{1}{2 x} - 6 x - \frac{16}{x ^{3}}

Simplify

\frac{1}{2 x} - 6 x - \frac{16}{x ^{3}} : \frac{x ^{\frac{5}{2}} - 32 - 12 x ^{4}}{2 x ^{\frac{5}{2}} x}

= \frac{x ^{\frac{5}{2}} - 32 - 12 x ^{4}}{2 x ^{\frac{5}{2}} x}

\frac{d y}{d x} = y + 4 y \cdot cos (2 x)

\int - 1728 - x^{3} d x

\int_{4}^{8} \frac{5}{12 - x} d x

\frac{d}{d x} ((arctan (5 x))^{2})

\int \frac{x ^{4} + 8 x ^{2} + 8}{x ^{3} - 4 x} d x

What is the derivative of sqrt(x)-3x^2+8x^{-2} ?
The derivative of sqrt(x)-3x^2+8x^{-2} is (x^{5/2}-32-12x^4)/(2x^{5/2)sqrt(x)}
What is the first derivative of sqrt(x)-3x^2+8x^{-2} ?
The first derivative of sqrt(x)-3x^2+8x^{-2} is (x^{5/2}-32-12x^4)/(2x^{5/2)sqrt(x)}