What is the derivative of arcsin(x^3+1) ?

The derivative of arcsin(x^3+1) is (3x^2)/(sqrt(-x^6-2x^3))

What is the first derivative of arcsin(x^3+1) ?

The first derivative of arcsin(x^3+1) is (3x^2)/(sqrt(-x^6-2x^3))

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derivative of

arcsin (x^{3} + 1)

\frac{3 x ^{2}}{- x ^{6} - 2 x ^{3}}

Solution steps

\frac{d}{d x} (arcsin (x^{3} + 1))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2}}{- x ^{6} - 2 x ^{3}}

arctan (\frac{6}{x})

1 + ln (x^{2})

13 x^{2} + 26 x + 15

2 x - y + 1

2 x - y

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