What is the derivative of arcsin(1+2x^2) ?

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

What is the first derivative of arcsin(1+2x^2) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - ( 1 + 2 x ^{2} ) ^{2}} \cdot 4 x : \frac{2 2}{- 2 x ^{2} - 2}

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

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