What is the derivative of (8+xf(x))/(sqrt(x)) ?

The derivative of (8+xf(x))/(sqrt(x)) is (3x^2f-8)/(2xsqrt(x))

What is the first derivative of (8+xf(x))/(sqrt(x)) ?

The first derivative of (8+xf(x))/(sqrt(x)) is (3x^2f-8)/(2xsqrt(x))

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derivative of

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

\frac{3 x ^{2} f - 8}{2 x x}

Solution steps

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

Treat

f

as a constant

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) = 2 f x

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

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

Simplify

\frac{2 f x x - \frac{1}{2 x} ( 8 + x f x )}{( x ) ^{2}} : \frac{3 x ^{2} f - 8}{2 x x}

= \frac{3 x ^{2} f - 8}{2 x x}

What is the derivative of (8+xf(x))/(sqrt(x)) ?
The derivative of (8+xf(x))/(sqrt(x)) is (3x^2f-8)/(2xsqrt(x))
What is the first derivative of (8+xf(x))/(sqrt(x)) ?
The first derivative of (8+xf(x))/(sqrt(x)) is (3x^2f-8)/(2xsqrt(x))