What is the derivative of (1+xf(x))/(sqrt(x)) ?

The derivative of (1+xf(x))/(sqrt(x)) is (3x^2f-1)/(2xsqrt(x))

What is the first derivative of (1+xf(x))/(sqrt(x)) ?

The first derivative of (1+xf(x))/(sqrt(x)) is (3x^2f-1)/(2xsqrt(x))

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derivative of

\frac{1 + x f ( x )}{x}

\frac{3 x ^{2} f - 1}{2 x x}

Solution steps

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

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

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

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

Simplify

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

= \frac{3 x ^{2} f - 1}{2 x x}

\int \frac{1}{2 - 3 u - u ^{2}} d u

\frac{d}{d x} (lo g_{2} (x + 1))

7 x^{2}

(x^{4})^{^{'}}

\frac{\partial}{\partial x} (\frac{1}{2} y arctan (\frac{x}{y}))

What is the derivative of (1+xf(x))/(sqrt(x)) ?
The derivative of (1+xf(x))/(sqrt(x)) is (3x^2f-1)/(2xsqrt(x))
What is the first derivative of (1+xf(x))/(sqrt(x)) ?
The first derivative of (1+xf(x))/(sqrt(x)) is (3x^2f-1)/(2xsqrt(x))