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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{\partial}{\partial x} (4 x - 8 y^{3})

y^{^{''}} - 6 y = 0

\frac{x ^{2}}{x - 4}

\frac{d}{d x} (2 sin (x) + 2 sin (x) cos (x))

3^{x}

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