en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(x){f}(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = f (x)

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

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

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

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

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

Popular Examples

((dy)/(dx))=sqrt(y+2x+5)-2

(\frac{d y}{d x}) = y + 2 x + 5 - 2

integral of (x+sqrt(5x-4))/(15x+9)

\int \frac{x + 5 x - 4}{15 x + 9} d x

5y^{''}+y^'=-4x

5 y^{^{''}} + y^{^{'}} = - 4 x

integral of (5x^4)/(1+x^{10)}

\int \frac{5 x ^{4}}{1 + x ^{10}} d x

integral of sqrt(x^2-6x+10)

\int x^{2} - 6 x + 10 d x

Frequently Asked Questions (FAQ)

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