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Popular Calculus >

derivative of arcsin(2x-1)

Solution

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

Solution

\frac{1}{x ( - x + 1 )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x ( - x + 1 )}

Graph

Popular Examples

y^{''}-2y^'-3y=3e^{2t},y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

limit as x approaches infinity of 1/3

x \to \infty lim (\frac{1}{3})

(dy)/(dx)+2y-8e^{-x}=0,y(0)=7

\frac{d y}{d x} + 2 y - 8 e^{- x} = 0, y (0) = 7

integral from 0 to 1 of (e^x)-(xe^{x^2})

\int_{0}^{1} (e^{x}) - (x e^{x^{2}}) d x

integral of (1+x^2)/(x-x^3)

\int \frac{1 + x ^{2}}{x - x ^{3}} d x

Frequently Asked Questions (FAQ)

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