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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

2 x lo g_{4} (x)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 z^{3})

\int \frac{2}{3} e^{3 x} x d x

\frac{d}{d x} (x^{4} + 5 x)

\frac{\partial}{\partial y} (x^{4} y - 2 x^{3} y^{2})

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