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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

ln (x), 5

x \to - \infty lim (x^{n})

F (x) = \frac{x ^{3} - 3 x ^{2} + 4 x - 5}{x ^{2}}

f (x) = e^{- x^{2}} + x

y^{^{'}} + 4 y = x^{2} e^{- 4 x}

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