What is the derivative of 8xarcsin(x) ?

The derivative of 8xarcsin(x) is 8(arcsin(x)+x/(sqrt(1-x^2)))

What is the first derivative of 8xarcsin(x) ?

The first derivative of 8xarcsin(x) is 8(arcsin(x)+x/(sqrt(1-x^2)))

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\frac{d}{d x} (8 x arcsin (x))

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

Solution steps

\frac{d}{d x} (8 x arcsin (x))

Take the constant out:

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

= 8 \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)

= 8 (\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}}

= 8 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Simplify

8 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 8 (arcsin (x) + \frac{x}{1 - x ^{2}})

= 8 (arcsin (x) + \frac{x}{1 - x ^{2}})

\frac{d}{d x} (3 x ln (9 x^{2}))

x \to 0 lim (e^{(\frac{1}{x})})

\int (1 + (\frac{1}{2}) \cdot \frac{2}{( 2 \cdot x + 3 )}) d x

\frac{d}{d x} (\frac{sin ( x ^{2} )}{sin ^{2} ( x )})

y = 6 x^{2} e^{- x}

What is the derivative of 8xarcsin(x) ?
The derivative of 8xarcsin(x) is 8(arcsin(x)+x/(sqrt(1-x^2)))
What is the first derivative of 8xarcsin(x) ?
The first derivative of 8xarcsin(x) is 8(arcsin(x)+x/(sqrt(1-x^2)))