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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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

= 2 (\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}

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

Simplify

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

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

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