en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xsqrt(3+x^2)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

derivative of tan(x)-sin(x)derivative of

tan (x) - sin (x)

(\partial)/(\partial x)(ln(x+8y+7z))

\frac{\partial}{\partial x} (ln (x + 8 y + 7 z))

integral of (1/(t^2)+sqrt(t))

\int (\frac{1}{t ^{2}} + t) d t

integral of (7/x-3/(x^2))

\int (\frac{7}{x} - \frac{3}{x ^{2}}) d x

integral of (3x^5-8)^96x^4

\int (3 x^{5} - 8)^{9} 6 x^{4} d x

Frequently Asked Questions (FAQ)

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