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Popular >

derivative of arcsin(sqrt(2x))

Solution

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

Solution

\frac{1}{2 x 1 - 2 x}

Solution steps

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

Simplify

arcsin (2 x) : arcsin (2 x)

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x) = \frac{1}{2 x}

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

Simplify

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

= \frac{1}{2 x 1 - 2 x}

Popular Examples

(\partial)/(\partial x)(yln(x))

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

integral of 12t^3

\int 12 t^{3} d t

(\partial)/(\partial x)(x^2y+xy^2+20)

\frac{\partial}{\partial x} (x^{2} y + x y^{2} + 20)

derivative of x^{0.7}y^{0.3}

\frac{d}{d x} (x^{0.7} y^{0.3})

d/(dy)(3cos(3x)(x-y)+sin(3x))

\frac{d}{d y} (3 cos (3 x) (x - y) + sin (3 x))

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(sqrt(2x)) ?
The derivative of arcsin(sqrt(2x)) is 1/(sqrt(2)\sqrt{x)sqrt(1-2x)}
What is the first derivative of arcsin(sqrt(2x)) ?
The first derivative of arcsin(sqrt(2x)) is 1/(sqrt(2)\sqrt{x)sqrt(1-2x)}