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Popular Calculus >

derivative of 3arcsin(x^3)

Solution

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

Solution

\frac{9 x ^{2}}{1 - x ^{6}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

3 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{9 x ^{2}}{1 - x ^{6}}

= \frac{9 x ^{2}}{1 - x ^{6}}

Graph

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\frac{\partial}{\partial w} (x e^{w})

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Frequently Asked Questions (FAQ)

What is the derivative of 3arcsin(x^3) ?
The derivative of 3arcsin(x^3) is (9x^2)/(sqrt(1-x^6))
What is the first derivative of 3arcsin(x^3) ?
The first derivative of 3arcsin(x^3) is (9x^2)/(sqrt(1-x^6))