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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (e^{x y^{2}} 2 x y)

\frac{\partial}{\partial x} (c e^{- 2 x} + e^{- x})

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

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

x \to 0 lim (1 - \frac{x ^{2}}{6})

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