What is the derivative of arcsin(5x^2) ?

The derivative of arcsin(5x^2) is (10x)/(sqrt(1-25x^4))

What is the first derivative of arcsin(5x^2) ?

The first derivative of arcsin(5x^2) is (10x)/(sqrt(1-25x^4))

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\frac{d}{d x} (arcsin (5 x^{2}))

\frac{10 x}{1 - 25 x ^{4}}

Solution steps

\frac{d}{d x} (arcsin (5 x^{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{2}) = 10 x

= \frac{1}{1 - ( 5 x ^{2} ) ^{2}} \cdot 10 x

Simplify

\frac{1}{1 - ( 5 x ^{2} ) ^{2}} \cdot 10 x : \frac{10 x}{1 - 25 x ^{4}}

= \frac{10 x}{1 - 25 x ^{4}}

What is the derivative of arcsin(5x^2) ?
The derivative of arcsin(5x^2) is (10x)/(sqrt(1-25x^4))
What is the first derivative of arcsin(5x^2) ?
The first derivative of arcsin(5x^2) is (10x)/(sqrt(1-25x^4))