What is the derivative of sqrt(x^9) ?

The derivative of sqrt(x^9) is (9x^{7/2})/2

What is the first derivative of sqrt(x^9) ?

The first derivative of sqrt(x^9) is (9x^{7/2})/2

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derivative of

x^{9}

\frac{9 x ^{\frac{7}{2}}}{2}

Solution steps

\frac{d}{d x} (x^{9})

Apply radical rule:

n a^{m} = a^{\frac{m}{n}}

= \frac{d}{d x} (x^{\frac{9}{2}})

Apply the Power Rule:

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

= \frac{9}{2} x^{\frac{9}{2} - 1}

Simplify

\frac{9}{2} x^{\frac{9}{2} - 1} : \frac{9 x ^{\frac{7}{2}}}{2}

= \frac{9 x ^{\frac{7}{2}}}{2}

\frac{d}{d x} (x + 2 x^{\frac{1}{3}})

\int \frac{cos ( \frac{π}{x ^{43}} )}{x ^{44}} d x

\frac{d}{d x} (x^{3} (4 x^{2} - 5 x - 6))

2 (1 - e^{- 5 t})

x \to 2 lim (2 x^{2} - 8)

What is the derivative of sqrt(x^9) ?
The derivative of sqrt(x^9) is (9x^{7/2})/2
What is the first derivative of sqrt(x^9) ?
The first derivative of sqrt(x^9) is (9x^{7/2})/2