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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{ln ( x )}{x ^{7}})

\int_{1}^{3} 17 r^{3} ln (r) d r

y^{^{'}} - \frac{6 y}{x} = x^{6} e^{x}

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

x \to 3 lim (csc (\frac{π x}{4}))

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