What is the derivative of f(x)=(x+sqrt(x))/(x^3) ?

The derivative of f(x)=(x+sqrt(x))/(x^3) is (-4x-5sqrt(x))/(2x^4)

What is the first derivative of f(x)=(x+sqrt(x))/(x^3) ?

The first derivative of f(x)=(x+sqrt(x))/(x^3) is (-4x-5sqrt(x))/(2x^4)

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derivative of

f (x) = \frac{x + x}{x ^{3}}

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

Solution steps

\frac{d}{d x} (\frac{x + x}{x ^{3}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{y}{y + x ^{2}})

\frac{d}{d x} (e^{x^{2}} sin (x))

\frac{d x}{d t} = 2 x (10 - x)

\frac{\partial}{\partial t} (e^{t} sin (t))

\frac{d}{d x} (3 ln (4 x))

What is the derivative of f(x)=(x+sqrt(x))/(x^3) ?
The derivative of f(x)=(x+sqrt(x))/(x^3) is (-4x-5sqrt(x))/(2x^4)
What is the first derivative of f(x)=(x+sqrt(x))/(x^3) ?
The first derivative of f(x)=(x+sqrt(x))/(x^3) is (-4x-5sqrt(x))/(2x^4)