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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

4^{- 3}

1.6 \cdot 1 0^{- 19} \cdot 400

2.21 \cdot 1 0^{- 4}

\frac{x ^{2}}{( 12.2 - 2 x ) ^{2}}

\frac{π}{2 π}

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