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))

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derivative of

3 arcsin (x^{3})

\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}}

\frac{d v}{d t} = v^{2} + 5 v + 6

f (x) = x \cdot ln (x) - x

x \to 0 lim (x^{- 1} - 1)

y = 8 x - x^{2}, y = 0

a sin (t)

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))