What is the derivative of y=(3+xf(x))/(sqrt(x)) ?

The derivative of y=(3+xf(x))/(sqrt(x)) is (2x^2\frac{df)/(dx)+xf(x)-3}{2xsqrt(x)}

What is the first derivative of y=(3+xf(x))/(sqrt(x)) ?

The first derivative of y=(3+xf(x))/(sqrt(x)) is (2x^2\frac{df)/(dx)+xf(x)-3}{2xsqrt(x)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

\frac{d}{d x} (3 + x f (x)) = x \frac{df}{d x} + f (x)

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

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

Simplify

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

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

x \to - \infty lim (- 1)

\int_{- 3}^{4} ∣ x ∣ d x

\int 11 - e^{3 x - 6} - 10 d x

\frac{d}{d x} (x (x^{5} + 5)^{3})

\int_{0}^{6} \frac{1}{36 + t ^{2}} d t

What is the derivative of y=(3+xf(x))/(sqrt(x)) ?
The derivative of y=(3+xf(x))/(sqrt(x)) is (2x^2\frac{df)/(dx)+xf(x)-3}{2xsqrt(x)}
What is the first derivative of y=(3+xf(x))/(sqrt(x)) ?
The first derivative of y=(3+xf(x))/(sqrt(x)) is (2x^2\frac{df)/(dx)+xf(x)-3}{2xsqrt(x)}