What is the derivative of 3xarcsin(x) ?

The derivative of 3xarcsin(x) is 3(arcsin(x)+x/(sqrt(1-x^2)))

What is the first derivative of 3xarcsin(x) ?

The first derivative of 3xarcsin(x) is 3(arcsin(x)+x/(sqrt(1-x^2)))

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derivative of

3 x arcsin (x)

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

Solution steps

\frac{d}{d x} (3 x arcsin (x))

Take the constant out:

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

= 3 \frac{d}{d x} (x arcsin (x))

Apply the Product Rule:

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

f = x, g = arcsin (x)

= 3 (\frac{d x}{d x} arcsin (x) + \frac{d}{d x} (arcsin (x)) x)

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

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

= 3 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Simplify

3 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 3 (arcsin (x) + \frac{x}{1 - x ^{2}})

= 3 (arcsin (x) + \frac{x}{1 - x ^{2}})

\frac{d}{d x} (\frac{2 ( 3 x ^{4} - 5 )}{x ^{3}})

(- 2.2) (0)

y = 6 x^{2}, y = x^{2} + 4

\frac{d}{d x} (3 + x^{2})

\frac{\partial}{\partial y} (arctan (x))

What is the derivative of 3xarcsin(x) ?
The derivative of 3xarcsin(x) is 3(arcsin(x)+x/(sqrt(1-x^2)))
What is the first derivative of 3xarcsin(x) ?
The first derivative of 3xarcsin(x) is 3(arcsin(x)+x/(sqrt(1-x^2)))