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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'}} = - 2 x tan (y), y (0) = \frac{π}{2}

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

\frac{d}{d x} (tan (x) ln (x))

x \to 3 lim (4 x^{3} - 3 x^{2} + x - 5)

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

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