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Popular >

derivative of f(x)=xsqrt(1+x^2)

Solution

derivative of

f (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}}

Popular Examples

y^{^{'}} + \frac{2}{t} y = 0

integral of (e^{-2x})/(1+e^{-x)}

\int \frac{e ^{- 2 x}}{1 + e ^{- x}} d x

(\partial)/(\partial x)(3x^2-2xy+x-3y)

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

sum from n=0 to infinity of 1/(n^2+3)

n = 0 \sum \infty \frac{1}{n ^{2} + 3}

limit as x approaches 1 of-x^2

x \to 1 lim (- x^{2})

Frequently Asked Questions (FAQ)

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