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Popular >

derivative of xsqrt(1+x^2)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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