What is the derivative of arcsin(5x^4) ?

The derivative of arcsin(5x^4) is (20x^3)/(sqrt(1-25x^8))

What is the first derivative of arcsin(5x^4) ?

The first derivative of arcsin(5x^4) is (20x^3)/(sqrt(1-25x^8))

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\frac{d}{d x} (arcsin (5 x^{4}))

\frac{20 x ^{3}}{1 - 25 x ^{8}}

Solution steps

\frac{d}{d x} (arcsin (5 x^{4}))

Apply the chain rule:

\frac{1}{1 - ( 5 x ^{4} ) ^{2}} \frac{d}{d x} (5 x^{4})

= \frac{1}{1 - ( 5 x ^{4} ) ^{2}} \frac{d}{d x} (5 x^{4})

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

= \frac{1}{1 - ( 5 x ^{4} ) ^{2}} \cdot 20 x^{3}

Simplify

\frac{1}{1 - ( 5 x ^{4} ) ^{2}} \cdot 20 x^{3} : \frac{20 x ^{3}}{1 - 25 x ^{8}}

= \frac{20 x ^{3}}{1 - 25 x ^{8}}

\int ln (2 + x) d x

(- 1, 1), (1, - 2)

x \to 0 lim (\frac{tan ( 2 ) ( x )}{x})

2 x^{8} e^{x}

\int \frac{1}{4 x} d x

What is the derivative of arcsin(5x^4) ?
The derivative of arcsin(5x^4) is (20x^3)/(sqrt(1-25x^8))
What is the first derivative of arcsin(5x^4) ?
The first derivative of arcsin(5x^4) is (20x^3)/(sqrt(1-25x^8))