What is (\partial)/(\partial x)(arcsin(-2x^4)) ?

The answer to (\partial)/(\partial x)(arcsin(-2x^4)) is -(8x^3)/(sqrt(1-4x^8))

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(\partial)/(\partial x)(arcsin(-2x^4))

\frac{\partial}{\partial x} (arcsin (- 2 x^{4}))

- \frac{8 x ^{3}}{1 - 4 x ^{8}}

Solution steps

\frac{\partial}{\partial x} (arcsin (- 2 x^{4}))

Apply the chain rule:

\frac{1}{1 - ( - 2 x ^{4} ) ^{2}} \frac{\partial}{\partial x} (- 2 x^{4})

= \frac{1}{1 - ( - 2 x ^{4} ) ^{2}} \frac{\partial}{\partial x} (- 2 x^{4})

\frac{\partial}{\partial x} (- 2 x^{4}) = - 8 x^{3}

= \frac{1}{1 - ( - 2 x ^{4} ) ^{2}} (- 8 x^{3})

Simplify

\frac{1}{1 - ( - 2 x ^{4} ) ^{2}} (- 8 x^{3}) : - \frac{8 x ^{3}}{1 - 4 x ^{8}}

= - \frac{8 x ^{3}}{1 - 4 x ^{8}}

n \to 0 lim (\frac{sin ( n )}{n})

\frac{d y}{d x} = \frac{y}{x} + \frac{y ^{2}}{x ^{2}}

\int (4 x + 3) cos (x) d x

y^{^{''}} + 3 y^{^{'}} + 2 = 0

\int_{1}^{9} e^{x} d x

What is (\partial)/(\partial x)(arcsin(-2x^4)) ?
The answer to (\partial)/(\partial x)(arcsin(-2x^4)) is -(8x^3)/(sqrt(1-4x^8))