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Popular Calculus >

derivative of y=xarcsin(2x)

Solution

derivative of

y = x arcsin (2 x)

Solution

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}}

Graph

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Frequently Asked Questions (FAQ)

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))