What is the derivative of (1+x^{1/3}) ?

The derivative of (1+x^{1/3}) is 1/(3(1+x)^{2/3)}

What is the first derivative of (1+x^{1/3}) ?

The first derivative of (1+x^{1/3}) is 1/(3(1+x)^{2/3)}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + x) = 1

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

Simplify

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

x \to x lim (\frac{x ^{2} - 1}{x - 1})

y = sin (x^{3})

\int \frac{x ^{3} - x}{x ^{3}} d x

n = 0 \sum \infty (- 1 + \frac{1}{e})^{n}

\frac{d}{d θ} (3 sin (3 θ))

What is the derivative of (1+x^{1/3}) ?
The derivative of (1+x^{1/3}) is 1/(3(1+x)^{2/3)}
What is the first derivative of (1+x^{1/3}) ?
The first derivative of (1+x^{1/3}) is 1/(3(1+x)^{2/3)}