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Popular Calculus >

derivative of y= 1/(sin^2(x))

Solution

derivative of

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

Solution

- 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)

Graph

Popular Examples

(dy)/(dx)=7xcos(x^2)

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

integral of xe^{x^2}cos(x^2)

\int x e^{x^{2}} cos (x^{2}) d x

derivative of (1-2x/(3x^2))

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

derivative of ((x+5/(x^2+2))^2)

\frac{d}{d x} ((\frac{x + 5}{x ^{2} + 2})^{2})

(d^2)/(dx^2)(e^{6/x})

\frac{d ^{2}}{d x ^{2}} (e^{\frac{6}{x}})

Frequently Asked Questions (FAQ)

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)