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

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

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

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

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derivative of

3 x^{3}

\frac{3 3 x ^{\frac{3}{2}}}{2 x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 3 x ^{\frac{3}{2}}}{2 x ^{2}}

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