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Popular >

derivative of ((x^3/9)^2)

Solution

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

Solution

\frac{2 x ^{5}}{27}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{x ^{3}}{9} \cdot \frac{x ^{2}}{3} : \frac{2 x ^{5}}{27}

= \frac{2 x ^{5}}{27}

Popular Examples

(\partial)/(\partial y)(1/y)

\frac{\partial}{\partial y} (\frac{1}{y})

limit as x approaches 1 of cos(1/(x-1))

x \to 1 lim (cos (\frac{1}{x - 1}))

y^{^{''}} - 2 y^{^{'}} = 7 t

(\partial)/(\partial x)(x^{0.5}*y^{0.5}*z)

\frac{\partial}{\partial x} (x^{0.5} \cdot y^{0.5} \cdot z)

tangent of y=x^3-3x+3,(3,21)tangent of

y = x^{3} - 3 x + 3, (3, 21)

Frequently Asked Questions (FAQ)

What is the derivative of ((x^3/9)^2) ?
The derivative of ((x^3/9)^2) is (2x^5)/(27)
What is the first derivative of ((x^3/9)^2) ?
The first derivative of ((x^3/9)^2) is (2x^5)/(27)