What is the derivative of (8+x{f}(x)/(sqrt(x))) ?

The derivative of (8+x{f}(x)/(sqrt(x))) is (2x^2 derivative of {f}(x)+x{f}(x)-8)/(2xsqrt(x))

What is the first derivative of (8+x{f}(x)/(sqrt(x))) ?

The first derivative of (8+x{f}(x)/(sqrt(x))) is (2x^2 derivative of {f}(x)+x{f}(x)-8)/(2xsqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{8 + x f ( x )}{x})

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

Solution steps

\frac{d}{d x} (\frac{8 + x f ( x )}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (8 + x f (x)) = x \frac{d}{d x} (f (x)) + f (x)

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

= \frac{( x \frac{d}{d x} ( f ( x ) ) + f ( x ) ) x - \frac{1}{2 x} ( 8 + x f ( x ) )}{( x ) ^{2}}

Simplify

\frac{( x \frac{d}{d x} ( f ( x ) ) + f ( x ) ) x - \frac{1}{2 x} ( 8 + x f ( x ) )}{( x ) ^{2}} : \frac{2 x ^{2} \frac{d}{d x} ( f ( x ) ) + x f ( x ) - 8}{2 x x}

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

\int sin (x) \frac{1}{x} d x

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

\frac{d y}{d x} = x \cdot e^{- 2 x}, y (0) = 3

\int sin (n x) d x

What is the derivative of (8+x{f}(x)/(sqrt(x))) ?
The derivative of (8+x{f}(x)/(sqrt(x))) is (2x^2 derivative of {f}(x)+x{f}(x)-8)/(2xsqrt(x))
What is the first derivative of (8+x{f}(x)/(sqrt(x))) ?
The first derivative of (8+x{f}(x)/(sqrt(x))) is (2x^2 derivative of {f}(x)+x{f}(x)-8)/(2xsqrt(x))