en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 2x(4x+9^{1/2}+12)

Solution

\frac{d}{d x} (2 x (4 x + 9)^{\frac{1}{2}} + 12)

Solution

\frac{2 ( 6 x + 9 )}{( 4 x + 9 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (2 x (4 x + 9)^{\frac{1}{2}} + 12)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x (4 x + 9)^{\frac{1}{2}}) + \frac{d}{d x} (12)

\frac{d}{d x} (2 x (4 x + 9)^{\frac{1}{2}}) = \frac{2 ( 6 x + 9 )}{( 4 x + 9 ) ^{\frac{1}{2}}}

\frac{d}{d x} (12) = 0

= \frac{2 ( 6 x + 9 )}{( 4 x + 9 ) ^{\frac{1}{2}}} + 0

Simplify

= \frac{2 ( 6 x + 9 )}{( 4 x + 9 ) ^{\frac{1}{2}}}

Graph

Popular Examples

derivative of (x^2+x*(tan(x)))

\frac{d}{d x} ((x^{2} + x) \cdot (tan (x)))

derivative of arcsin(-x)

\frac{d}{d x} (arcsin (- x))

derivative of 6sec(x^2)

\frac{d}{d x} (6 sec (x^{2}))

derivative of (410t)/((t^2+5)^3)derivative of

\frac{410 t}{( t ^{2} + 5 ) ^{3}}

derivative of (4-3x-x^2/(x-2))

\frac{d}{d x} (\frac{4 - 3 x - x ^{2}}{x - 2})

Frequently Asked Questions (FAQ)

What is the derivative of 2x(4x+9^{1/2}+12) ?
The derivative of 2x(4x+9^{1/2}+12) is (2(6x+9))/((4x+9)^{1/2)}
What is the first derivative of 2x(4x+9^{1/2}+12) ?
The first derivative of 2x(4x+9^{1/2}+12) is (2(6x+9))/((4x+9)^{1/2)}