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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

= \frac{1}{2 x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

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

= \frac{1}{2 x ^{2} + 5 x} (2 x + 5)

Simplify

\frac{1}{2 x ^{2} + 5 x} (2 x + 5) : \frac{2 x + 5}{2 x ^{2} + 5 x}

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

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