What is the derivative of sqrt(x^n) ?

The derivative of sqrt(x^n) is (nx^{(n-2)/2})/(2)

What is the first derivative of sqrt(x^n) ?

The first derivative of sqrt(x^n) is (nx^{(n-2)/2})/(2)

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\frac{d}{d x} (x^{n})

\frac{n x ^{\frac{n - 2}{2}}}{2}

Solution steps

\frac{d}{d x} (x^{n})

Apply radical rule:

= \frac{d}{d x} (x^{\frac{n}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{n}{2} x^{\frac{n}{2} - 1}

Simplify

\frac{n}{2} x^{\frac{n}{2} - 1} : \frac{n x ^{\frac{n - 2}{2}}}{2}

= \frac{n x ^{\frac{n - 2}{2}}}{2}

10 x^{2} sin (8 x)

\frac{d}{d x} (4 x + 10)

\int_{2}^{6} (\frac{x}{2} + 1) d x

\frac{d y}{d x} = 2 x y

y^{^{''}} + 6 y^{^{'}} + 90 y = 0

What is the derivative of sqrt(x^n) ?
The derivative of sqrt(x^n) is (nx^{(n-2)/2})/(2)
What is the first derivative of sqrt(x^n) ?
The first derivative of sqrt(x^n) is (nx^{(n-2)/2})/(2)