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Popular >

derivative of x*sqrt(x^2+1)

Solution

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

Solution

\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}

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\frac{d}{d x} (\frac{x}{sin ( x )})

(\partial)/(\partial x)(x^{1/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}})

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x \to 1 lim (2 x + 3)

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\int cos (2 x) cos (6 x) d x

Frequently Asked Questions (FAQ)

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