What is the derivative of arccsc(2x+1) ?

The derivative of arccsc(2x+1) is -1/((2x+1)sqrt(x(x+1)))

What is the first derivative of arccsc(2x+1) ?

The first derivative of arccsc(2x+1) is -1/((2x+1)sqrt(x(x+1)))

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\frac{d}{d x} (arccsc (2 x + 1))

- \frac{1}{( 2 x + 1 ) x ( x + 1 )}

Solution steps

\frac{d}{d x} (arccsc (2 x + 1))

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (sin (x))^{3} (cos (x)) d x

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

x \to 0 lim (e^{7 x})

\int arccos (7 x) d x

n = 0 \sum \infty n + 2

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