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

The derivative of 1+cot^2(x) is -2csc^2(x)cot(x)

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

The first derivative of 1+cot^2(x) is -2csc^2(x)cot(x)

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

- 2 csc^{2} (x) cot (x)

Solution steps

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

Simplify

1 + cot^{2} (x) : csc^{2} (x)

= \frac{d}{d x} (csc^{2} (x))

Apply the chain rule:

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

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= 2 csc (x) (- cot (x) csc (x))

Simplify

2 csc (x) (- cot (x) csc (x)) : - 2 csc^{2} (x) cot (x)

= - 2 csc^{2} (x) cot (x)

x \to 0 lim (\frac{x}{- 2 x ^{4} - 14 x})

x \to - 2 lim (\frac{x ^{2}}{x ^{2} - 4})

\int \frac{1}{x ^{2} + y ^{2}} d x

\int sin^{4} (8 x) d x

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

What is the derivative of 1+cot^2(x) ?
The derivative of 1+cot^2(x) is -2csc^2(x)cot(x)
What is the first derivative of 1+cot^2(x) ?
The first derivative of 1+cot^2(x) is -2csc^2(x)cot(x)