What is the derivative of f(x)=xsqrt(x^2+1) ?

The derivative of f(x)=xsqrt(x^2+1) is (2x^2+1)/(sqrt(x^2+1))

What is the first derivative of f(x)=xsqrt(x^2+1) ?

The first derivative of f(x)=xsqrt(x^2+1) is (2x^2+1)/(sqrt(x^2+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = x x^{2} + 1

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{2} + 1

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

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

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

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

Simplify

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

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

(t^{2} - 1)^{2}

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

x \to - 19 + lim (x + 19)

y = arccos (2 x)

\int e^{in x} d x

What is the derivative of f(x)=xsqrt(x^2+1) ?
The derivative of f(x)=xsqrt(x^2+1) is (2x^2+1)/(sqrt(x^2+1))
What is the first derivative of f(x)=xsqrt(x^2+1) ?
The first derivative of f(x)=xsqrt(x^2+1) is (2x^2+1)/(sqrt(x^2+1))