What is the derivative of y= 1/(sin^2(x)) ?

The derivative of y= 1/(sin^2(x)) is -2csc^2(x)cot(x)

What is the first derivative of y= 1/(sin^2(x)) ?

The first derivative of y= 1/(sin^2(x)) is -2csc^2(x)cot(x)

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derivative of

y = \frac{1}{sin ^{2} ( x )}

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

Solution steps

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

Simplify

\frac{1}{sin ^{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)

\frac{d y}{d x} = 7 x cos (x^{2})

\frac{d y}{d x} = 8 y, y (6) = 7

\int \frac{x + 2}{x + 4} d x

y = 5 x^{3} + 25 x^{2} - π

\int_{0}^{1} 21 \frac{1}{x ^{p}} d x

What is the derivative of y= 1/(sin^2(x)) ?
The derivative of y= 1/(sin^2(x)) is -2csc^2(x)cot(x)
What is the first derivative of y= 1/(sin^2(x)) ?
The first derivative of y= 1/(sin^2(x)) is -2csc^2(x)cot(x)