What is the derivative of sqrt(4/9 x^3) ?

The derivative of sqrt(4/9 x^3) is sqrt(x)

What is the first derivative of sqrt(4/9 x^3) ?

The first derivative of sqrt(4/9 x^3) is sqrt(x)

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\frac{d}{d x} (\frac{4}{9} x^{3})

x

Solution steps

\frac{d}{d x} (\frac{4}{9} x^{3})

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{4}{9} x ^{3}} \cdot \frac{4 x ^{2}}{3}

Simplify

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

= x

What is the derivative of sqrt(4/9 x^3) ?
The derivative of sqrt(4/9 x^3) is sqrt(x)
What is the first derivative of sqrt(4/9 x^3) ?
The first derivative of sqrt(4/9 x^3) is sqrt(x)