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

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

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

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

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Popular >

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

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

Solution steps

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

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}}

\int_{0}^{27} \frac{3}{x ^{\frac{2}{3}}} d x

11 e^{x^{2}}

\int - 1 (x - 4) d x

t \to π lim (\frac{t}{π})

\frac{d}{d x} ((2 x^{2} + 7) (8 x - 4))

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