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

The derivative of [((x-1))/((x+3))]^{1/3} is 4/(3(x-1)^{2/3)(x+3)^{4/3}}

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

The first derivative of [((x-1))/((x+3))]^{1/3} is 4/(3(x-1)^{2/3)(x+3)^{4/3}}

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derivative of

[\frac{( x - 1 )}{( x + 3 )}]^{\frac{1}{3}}

\frac{4}{3 ( x - 1 ) ^{\frac{2}{3}} ( x + 3 ) ^{\frac{4}{3}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x - 1}{x + 3}) = \frac{4}{( x + 3 ) ^{2}}

= \frac{1}{3 ( \frac{x - 1}{x + 3} ) ^{\frac{2}{3}}} \cdot \frac{4}{( x + 3 ) ^{2}}

Simplify

\frac{1}{3 ( \frac{x - 1}{x + 3} ) ^{\frac{2}{3}}} \cdot \frac{4}{( x + 3 ) ^{2}} : \frac{4}{3 ( x - 1 ) ^{\frac{2}{3}} ( x + 3 ) ^{\frac{4}{3}}}

= \frac{4}{3 ( x - 1 ) ^{\frac{2}{3}} ( x + 3 ) ^{\frac{4}{3}}}

\int \frac{1}{- x ^{2} + 6 x + 7} d x

\int 5 x^{- 3} + 4 x^{- 2} - 3 x^{- 1} + 4 d x

\int_{0}^{1} 1 + \frac{9 x}{4} d x

cos (t) y^{^{'}} + sin (t) y = 2 cos^{3} (t) sin (t) - 1

\frac{c}{x}

What is the derivative of [((x-1))/((x+3))]^{1/3} ?
The derivative of [((x-1))/((x+3))]^{1/3} is 4/(3(x-1)^{2/3)(x+3)^{4/3}}
What is the first derivative of [((x-1))/((x+3))]^{1/3} ?
The first derivative of [((x-1))/((x+3))]^{1/3} is 4/(3(x-1)^{2/3)(x+3)^{4/3}}