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Popular >

derivative of (d/(dx(x^3))^2)

Solution

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

Solution

36 x^{3}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{d}{d x} (x^{3})) = 6 x

= 2 \frac{d}{d x} (x^{3}) 6 x

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot 3 x^{3 - 1} \cdot 6 x

Simplify

2 \cdot 3 x^{3 - 1} \cdot 6 x : 36 x^{3}

= 36 x^{3}

Graph

Popular Examples

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\frac{d}{d x} (cos^{2} (sin (2 x)))

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

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Frequently Asked Questions (FAQ)

What is the derivative of (d/(dx(x^3))^2) ?
The derivative of (d/(dx(x^3))^2) is 36x^3
What is the first derivative of (d/(dx(x^3))^2) ?
The first derivative of (d/(dx(x^3))^2) is 36x^3