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

The derivative of 1/3 (x^2+2^{2/3}) is (4x)/(9(x^2+2)^{1/3)}

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

The first derivative of 1/3 (x^2+2^{2/3}) is (4x)/(9(x^2+2)^{1/3)}

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

\frac{4 x}{9 ( x ^{2} + 2 ) ^{\frac{1}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{3} \cdot \frac{2}{3 ( x ^{2} + 2 ) ^{\frac{1}{3}}} \cdot 2 x : \frac{4 x}{9 ( x ^{2} + 2 ) ^{\frac{1}{3}}}

= \frac{4 x}{9 ( x ^{2} + 2 ) ^{\frac{1}{3}}}

n = 1 \sum \infty \frac{n ^{3}}{2 ^{n}}

\frac{d}{d x} (ln (x^{2}))

\frac{\partial}{\partial y} (x^{4} y + x z - y z^{2} - 7)

\frac{d y}{d x} = e^{6 y} e^{6 x}

\frac{d y}{d x} = y (y^{5} x + 2)

What is the derivative of 1/3 (x^2+2^{2/3}) ?
The derivative of 1/3 (x^2+2^{2/3}) is (4x)/(9(x^2+2)^{1/3)}
What is the first derivative of 1/3 (x^2+2^{2/3}) ?
The first derivative of 1/3 (x^2+2^{2/3}) is (4x)/(9(x^2+2)^{1/3)}