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))

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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}

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))