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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derivative of

\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}}

\int \frac{( x ^{2} - x + 36 )}{x ^{3} + 6 x} d x

y = 2 sin (x), (\frac{π}{6}, 1)

x \to 2 + lim (\frac{x ^{2}}{x ^{2} - 4})

1 - (1 - 0.01 x)^{3}

\int_{0}^{1} 11 x x^{2} + 16 d 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}