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} \cdot 1

Simplify

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

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

\frac{\partial}{\partial x} (4 y cos (x y))

x tan (x)

\int_{\frac{π}{2}}^{π} sin^{2} (x) d x

5 - 4 x^{3}

{y}

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}