What is the derivative of y=(arcsin(x^3))^4 ?

The derivative of y=(arcsin(x^3))^4 is (12x^2arcsin^3(x^3))/(sqrt(1-x^6))

What is the first derivative of y=(arcsin(x^3))^4 ?

The first derivative of y=(arcsin(x^3))^4 is (12x^2arcsin^3(x^3))/(sqrt(1-x^6))

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derivative of

y = (arcsin (x^{3}))^{4}

\frac{12 x ^{2} arcsin ^{3} ( x ^{3} )}{1 - x ^{6}}

Solution steps

\frac{d}{d x} ((arcsin (x^{3}))^{4})

Apply the chain rule:

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

= 4 (arcsin (x^{3}))^{3} \frac{d}{d x} (arcsin (x^{3}))

\frac{d}{d x} (arcsin (x^{3})) = \frac{3 x ^{2}}{1 - x ^{6}}

= 4 (arcsin (x^{3}))^{3} \frac{3 x ^{2}}{1 - x ^{6}}

Simplify

4 arcsin^{3} (x^{3}) \frac{3 x ^{2}}{1 - x ^{6}} : \frac{12 x ^{2} arcsin ^{3} ( x ^{3} )}{1 - x ^{6}}

= \frac{12 x ^{2} arcsin ^{3} ( x ^{3} )}{1 - x ^{6}}

y = 3 x - 2

(1, 1), (4, - 16)

f (x) = e^{- x}

x

2 x^{2}

What is the derivative of y=(arcsin(x^3))^4 ?
The derivative of y=(arcsin(x^3))^4 is (12x^2arcsin^3(x^3))/(sqrt(1-x^6))
What is the first derivative of y=(arcsin(x^3))^4 ?
The first derivative of y=(arcsin(x^3))^4 is (12x^2arcsin^3(x^3))/(sqrt(1-x^6))