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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

t^{3} e^{b \cdot t}

\frac{\partial}{\partial x} (ln (x + y^{4}))

x \to \infty lim (- \frac{x}{2})

x \to \frac{π}{2} lim (5 sin (x))

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