What is the derivative of (5sqrt(x)/(2x^{-2)}) ?

The derivative of (5sqrt(x)/(2x^{-2)}) is (25x^{3/2})/4

What is the first derivative of (5sqrt(x)/(2x^{-2)}) ?

The first derivative of (5sqrt(x)/(2x^{-2)}) is (25x^{3/2})/4

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

\frac{25 x ^{\frac{3}{2}}}{4}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{5}{2} \frac{d}{d x} (\frac{x}{x ^{- 2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{5}{2} \cdot \frac{\frac{d}{d x} ( x ) x ^{- 2} - \frac{d}{d x} ( x ^{- 2} ) x}{( x ^{- 2} ) ^{2}}

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

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

= \frac{5}{2} \cdot \frac{\frac{1}{2 x} x ^{- 2} - ( - \frac{2}{x ^{3}} ) x}{( x ^{- 2} ) ^{2}}

Simplify

\frac{5}{2} \cdot \frac{\frac{1}{2 x} x ^{- 2} - ( - \frac{2}{x ^{3}} ) x}{( x ^{- 2} ) ^{2}} : \frac{25 x ^{\frac{3}{2}}}{4}

= \frac{25 x ^{\frac{3}{2}}}{4}

x \to \infty lim (3 + x^{2})

2 y = 3 x, y = 4, 2 y + 3 x = 6

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

x \to 0 + lim ((3 x)^{s i n (x)})

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

What is the derivative of (5sqrt(x)/(2x^{-2)}) ?
The derivative of (5sqrt(x)/(2x^{-2)}) is (25x^{3/2})/4
What is the first derivative of (5sqrt(x)/(2x^{-2)}) ?
The first derivative of (5sqrt(x)/(2x^{-2)}) is (25x^{3/2})/4