Derivative of `sqrt(x)`

Step-by-step differentiation

Answer

\frac{d}{d x} [x]

\frac{\frac{1}{2}}{x}

Step-by-step solution

1Derivative of sqrt
$\frac{d}{d x} [x] = \frac{1}{2 x}$
The derivative of $x$ is $\frac{1}{2 x}$ .
✓Final Answer
$\frac{d}{d x} [x] = \frac{\frac{1}{2}}{x}$
The first derivative simplifies to $\frac{\frac{1}{2}}{x}$ .

Understanding this derivative

Differentiating sqrt(x) is a single-rule problem: everything follows from the square root rule. That makes it a good expression for isolating and practicing that one technique.

A square root is a power of one-half in disguise, so the power rule gives d/dx[√x] = 1/(2√x); the chain rule extends this to roots of larger expressions.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.

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Derivative of sqrt(x)

Step-by-step solution

Understanding this derivative

Derivative of `sqrt(x)`