What is the derivative of xsqrt(x^2+5) ?

The derivative of xsqrt(x^2+5) is (2x^2+5)/(sqrt(x^2+5))

What is the first derivative of xsqrt(x^2+5) ?

The first derivative of xsqrt(x^2+5) is (2x^2+5)/(sqrt(x^2+5))

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derivative of

x x^{2} + 5

\frac{2 x ^{2} + 5}{x ^{2} + 5}

Solution steps

\frac{d}{d x} (x x^{2} + 5)

Apply the Product Rule:

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

f = x, g = x^{2} + 5

= \frac{d x}{d x} x^{2} + 5 + \frac{d}{d x} (x^{2} + 5) x

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

\frac{d}{d x} (x^{2} + 5) = \frac{x}{x ^{2} + 5}

= 1 \cdot x^{2} + 5 + \frac{x}{x ^{2} + 5} x

Simplify

1 \cdot x^{2} + 5 + \frac{x}{x ^{2} + 5} x : \frac{2 x ^{2} + 5}{x ^{2} + 5}

= \frac{2 x ^{2} + 5}{x ^{2} + 5}

n = 2 \sum \infty \frac{1}{n}

\frac{d}{d x} (x^{- \frac{1}{5}})

\int \frac{x}{x ^{4} x ^{4} - x ^{2}} d x

\frac{d}{d x} (x^{0.9})

f (x) = (x + 1) (x + 1 - \frac{1}{x + 2})

What is the derivative of xsqrt(x^2+5) ?
The derivative of xsqrt(x^2+5) is (2x^2+5)/(sqrt(x^2+5))
What is the first derivative of xsqrt(x^2+5) ?
The first derivative of xsqrt(x^2+5) is (2x^2+5)/(sqrt(x^2+5))