What is the derivative of xsqrt(x^2+4) ?

The derivative of xsqrt(x^2+4) is (2x^2+4)/(sqrt(x^2+4))

What is the first derivative of xsqrt(x^2+4) ?

The first derivative of xsqrt(x^2+4) is (2x^2+4)/(sqrt(x^2+4))

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\frac{d}{d x} (x x^{2} + 4)

\frac{2 x ^{2} + 4}{x ^{2} + 4}

Solution steps

\frac{d}{d x} (x x^{2} + 4)

Apply the Product Rule:

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

f = x, g = x^{2} + 4

= \frac{d x}{d x} x^{2} + 4 + \frac{d}{d x} (x^{2} + 4) x

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

\frac{d}{d x} (x^{2} + 4) = \frac{x}{x ^{2} + 4}

= 1 \cdot x^{2} + 4 + \frac{x}{x ^{2} + 4} x

Simplify

1 \cdot x^{2} + 4 + \frac{x}{x ^{2} + 4} x : \frac{2 x ^{2} + 4}{x ^{2} + 4}

= \frac{2 x ^{2} + 4}{x ^{2} + 4}

What is the derivative of xsqrt(x^2+4) ?
The derivative of xsqrt(x^2+4) is (2x^2+4)/(sqrt(x^2+4))
What is the first derivative of xsqrt(x^2+4) ?
The first derivative of xsqrt(x^2+4) is (2x^2+4)/(sqrt(x^2+4))