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Popular >

derivative of arccsc(2x+1)

Solution

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

Solution

- \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 )}

Popular Examples

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x \to 0 lim (arctan (\frac{5}{x}))

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Frequently Asked Questions (FAQ)

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)))