What is the derivative of arcsin(2x-3) ?

The derivative of arcsin(2x-3) is 1/(sqrt(-x^2+3x-2))

What is the first derivative of arcsin(2x-3) ?

The first derivative of arcsin(2x-3) is 1/(sqrt(-x^2+3x-2))

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derivative of

arcsin (2 x - 3)

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

Solution steps

\frac{d}{d x} (arcsin (2 x - 3))

Apply the chain rule:

\frac{1}{1 - ( 2 x - 3 ) ^{2}} \frac{d}{d x} (2 x - 3)

= \frac{1}{1 - ( 2 x - 3 ) ^{2}} \frac{d}{d x} (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

= \frac{1}{1 - ( 2 x - 3 ) ^{2}} \cdot 2

Simplify

\frac{1}{1 - ( 2 x - 3 ) ^{2}} \cdot 2 : \frac{1}{- x ^{2} + 3 x - 2}

= \frac{1}{- x ^{2} + 3 x - 2}

\int \frac{x}{sec ( x )} d x

\frac{d y}{d x}, y^{x} = x^{y}

\frac{d y}{d t} - y = 1, y (0) = 0

t y^{^{'}} + y = 1 + y + y^{2}

\frac{d}{d x} (f (x) + g (x))

What is the derivative of arcsin(2x-3) ?
The derivative of arcsin(2x-3) is 1/(sqrt(-x^2+3x-2))
What is the first derivative of arcsin(2x-3) ?
The first derivative of arcsin(2x-3) is 1/(sqrt(-x^2+3x-2))