en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (2x+3^{1/2})

Solution

\frac{d}{d x} ((2 x + 3)^{\frac{1}{2}})

Solution

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

Solution steps

\frac{d}{d x} ((2 x + 3)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 2 x + 3 ) ^{\frac{1}{2}}} \frac{d}{d x} (2 x + 3)

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

\frac{d}{d x} (2 x + 3) = 2

= \frac{1}{2 ( 2 x + 3 ) ^{\frac{1}{2}}} \cdot 2

Simplify

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

= \frac{1}{( 2 x + 3 ) ^{\frac{1}{2}}}

Popular Examples

(\partial)/(\partial x)(3x^2y)

\frac{\partial}{\partial x} (3 x^{2} y)

derivative of sin(x-2)

\frac{d}{d x} (sin (x - 2))

derivative of ((4x-4^5)/((2x-5)^7))

\frac{d}{d x} (\frac{( 4 x - 4 ) ^{5}}{( 2 x - 5 ) ^{7}})

derivative of 38e^{x^2}x derivative of

38 e^{x^{2}} x

integral of 7/(sqrt(5-6x))

\int \frac{7}{5 - 6 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (2x+3^{1/2}) ?
The derivative of (2x+3^{1/2}) is 1/((2x+3)^{1/2)}
What is the first derivative of (2x+3^{1/2}) ?
The first derivative of (2x+3^{1/2}) is 1/((2x+3)^{1/2)}