What is the derivative of \sqrt[N+1]{X} ?

The derivative of \sqrt[N+1]{X} is (X^{-N/(N+1)})/(N+1)

What is the first derivative of \sqrt[N+1]{X} ?

The first derivative of \sqrt[N+1]{X} is (X^{-N/(N+1)})/(N+1)

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derivative of

N + 1 X

\frac{X ^{- \frac{N}{N + 1}}}{N + 1}

Solution steps

\frac{d}{d X} (N + 1 X)

Apply radical rule:

n a = a^{\frac{1}{n}}

= \frac{d}{d X} (X^{\frac{1}{N + 1}})

Apply the Power Rule:

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

= \frac{1}{N + 1} X^{\frac{1}{N + 1} - 1}

Simplify

\frac{1}{N + 1} X^{\frac{1}{N + 1} - 1} : \frac{X ^{- \frac{N}{N + 1}}}{N + 1}

= \frac{X ^{- \frac{N}{N + 1}}}{N + 1}

y^{^{''}} + 16 y = e^{2 t} tan (4 t)

x \to 2 lim ((x^{2} + 8) (2 x - 4))

y \to - \infty lim (\frac{2 - y}{7 + 6 y ^{2}})

\frac{\partial}{\partial y} (26 - x^{2} - 4 y^{2})

\int \frac{6 x}{7 - 3 x ^{2}} d x

What is the derivative of \sqrt[N+1]{X} ?
The derivative of \sqrt[N+1]{X} is (X^{-N/(N+1)})/(N+1)
What is the first derivative of \sqrt[N+1]{X} ?
The first derivative of \sqrt[N+1]{X} is (X^{-N/(N+1)})/(N+1)