What is the derivative of (arcsin(x)dx) ?

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

What is the first derivative of (arcsin(x)dx) ?

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

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\frac{d}{d x} ((arcsin (x)) d x)

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

Solution steps

\frac{d}{d x} ((arcsin (x)) d x)

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= d \frac{d}{d x} (arcsin (x) x)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = arcsin (x), g = x

= d (\frac{d}{d x} (arcsin (x)) x + \frac{d x}{d x} arcsin (x))

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\int \frac{1}{9 x ^{2} + 18 x + 10} d x

f (x) = \frac{x + 1}{x - 1}

f (x) = (\frac{3 x - 1}{2 x - 3})

\int_{0}^{1 - ∣ x - 1 ∣} 1 d y

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