What is the derivative of sqrt(x^2+45) ?

The derivative of sqrt(x^2+45) is x/(sqrt(x^2+45))

What is the first derivative of sqrt(x^2+45) ?

The first derivative of sqrt(x^2+45) is x/(sqrt(x^2+45))

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\frac{d}{d x} (x^{2} + 45)

\frac{x}{x ^{2} + 45}

Solution steps

\frac{d}{d x} (x^{2} + 45)

Apply the chain rule:

\frac{1}{2 x ^{2} + 45} \frac{d}{d x} (x^{2} + 45)

= \frac{1}{2 x ^{2} + 45} \frac{d}{d x} (x^{2} + 45)

\frac{d}{d x} (x^{2} + 45) = 2 x

= \frac{1}{2 x ^{2} + 45} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + 45} \cdot 2 x : \frac{x}{x ^{2} + 45}

= \frac{x}{x ^{2} + 45}

What is the derivative of sqrt(x^2+45) ?
The derivative of sqrt(x^2+45) is x/(sqrt(x^2+45))
What is the first derivative of sqrt(x^2+45) ?
The first derivative of sqrt(x^2+45) is x/(sqrt(x^2+45))