en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of {f}(xsqrt(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = f (x), g = x

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

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

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

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

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

Popular Examples

limit as x approaches-3+of (|x+3|)/(x+3)

x \to - 3 + lim (\frac{∣ x + 3 ∣}{x + 3})

derivative of 30e^{-0.0000323x}derivative of

30 e^{- 0.0000323 x}

integral from-4 to 0 of sqrt(y+4)

\int_{- 4}^{0} y + 4 d y

integral of (10x+2)/((3x+1)(x-1))

\int \frac{10 x + 2}{( 3 x + 1 ) ( x - 1 )} d x

integral of x^2+8

\int x^{2} + 8 d x

Frequently Asked Questions (FAQ)

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