What is the derivative of xsqrt(x^2+9) ?

The derivative of xsqrt(x^2+9) is (2x^2+9)/(sqrt(x^2+9))

What is the first derivative of xsqrt(x^2+9) ?

The first derivative of xsqrt(x^2+9) is (2x^2+9)/(sqrt(x^2+9))

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derivative of

x x^{2} + 9

\frac{2 x ^{2} + 9}{x ^{2} + 9}

Solution steps

\frac{d}{d x} (x x^{2} + 9)

Apply the Product Rule:

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

f = x, g = x^{2} + 9

= \frac{d x}{d x} x^{2} + 9 + \frac{d}{d x} (x^{2} + 9) x

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

\frac{d}{d x} (x^{2} + 9) = \frac{x}{x ^{2} + 9}

= 1 \cdot x^{2} + 9 + \frac{x}{x ^{2} + 9} x

Simplify

1 \cdot x^{2} + 9 + \frac{x}{x ^{2} + 9} x : \frac{2 x ^{2} + 9}{x ^{2} + 9}

= \frac{2 x ^{2} + 9}{x ^{2} + 9}

What is the derivative of xsqrt(x^2+9) ?
The derivative of xsqrt(x^2+9) is (2x^2+9)/(sqrt(x^2+9))
What is the first derivative of xsqrt(x^2+9) ?
The first derivative of xsqrt(x^2+9) is (2x^2+9)/(sqrt(x^2+9))