What is the derivative of y=xarcsin(2x) ?

The derivative of y=xarcsin(2x) is arcsin(2x)+(2x)/(sqrt(1-4x^2))

What is the first derivative of y=xarcsin(2x) ?

The first derivative of y=xarcsin(2x) is arcsin(2x)+(2x)/(sqrt(1-4x^2))

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derivative of

y = x arcsin (2 x)

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = arcsin (2 x)

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

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

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

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

Simplify

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

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

x (\frac{d y}{d x}) = x^{3} + 16 x^{3} y

\frac{\partial}{\partial x} (3 x^{3} y - \frac{4}{x} + 2 y^{\frac{1}{2}})

\int_{\frac{1}{7}}^{3} 8 x ln (7 x) d x

y = 3 x + 6 cos (x), at (\frac{π}{3})

\frac{s}{s ^{2} + 2 s + 3}

What is the derivative of y=xarcsin(2x) ?
The derivative of y=xarcsin(2x) is arcsin(2x)+(2x)/(sqrt(1-4x^2))
What is the first derivative of y=xarcsin(2x) ?
The first derivative of y=xarcsin(2x) is arcsin(2x)+(2x)/(sqrt(1-4x^2))