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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derivative of

\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}}

f (x) = 3 e^{x}, at x = 0

y^{^{'}} = - 5 y + 5 t^{2} + 2 t, y (0) = \frac{1}{3}

\int \frac{3}{4 - x ^{2}} d x

\frac{d}{d θ} (θ - sin (θ))

x \to 0 lim (\frac{1}{sin ( x )})

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}