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

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

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

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

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

x

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= x

\int_{- 4}^{- 2} (x^{2} - 4) d x

5 x^{2} + x

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

\int x sin (\frac{x}{2}) d x

f (t) = 4 t^{2} + 5

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