en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2sqrt(2x+3)

Solution

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

Solution

\frac{5 x ^{2} + 6 x}{2 x + 3}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 2 x + 3

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

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

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

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

Simplify

2 x 2 x + 3 + \frac{1}{2 x + 3} x^{2} : \frac{5 x ^{2} + 6 x}{2 x + 3}

= \frac{5 x ^{2} + 6 x}{2 x + 3}

Popular Examples

area x^2+4,-x^2-1,[-2,3]area

x^{2} + 4, - x^{2} - 1, [- 2, 3]

derivative of arcsec(x^{10})

\frac{d}{d x} (arcsec (x^{10}))

derivative of (cos(pix-16)^4)

\frac{d}{d x} ((cos (π x - 16))^{4})

integral of 1/(sqrt(-x^2-6x))

\int \frac{1}{- x ^{2} - 6 x} d x

area x=-y,x=2y+3,y=-2,y=1 area

x = - y, x = 2 y + 3, y = - 2, y = 1

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(2x+3) ?
The derivative of x^2sqrt(2x+3) is (5x^2+6x)/(sqrt(2x+3))
What is the first derivative of x^2sqrt(2x+3) ?
The first derivative of x^2sqrt(2x+3) is (5x^2+6x)/(sqrt(2x+3))