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Popular Calculus >

derivative of 2csc^2(x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Simplify

2 \cdot 2 csc (x) (- cot (x) csc (x)) : - 4 csc^{2} (x) cot (x)

= - 4 csc^{2} (x) cot (x)

Graph

Popular Examples

(\partial)/(\partial x)(x/(x^2+y^2)+2x)

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}} + 2 x)

integral of 4/x+x/(x^2+5)

\int \frac{4}{x} + \frac{x}{x ^{2} + 5} d x

tangent of y=3-9x^2

t an g e n t y = 3 - 9 x^{2}

implicit (dy)/(dx),e^xy=8

im pl i c i t \frac{d y}{d x}, e^{x} y = 8

y^'=((x^2y+y^3))/(x^3)

y^{^{'}} = \frac{( x ^{2} y + y ^{3} )}{x ^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of 2csc^2(x) ?
The derivative of 2csc^2(x) is -4csc^2(x)cot(x)
What is the first derivative of 2csc^2(x) ?
The first derivative of 2csc^2(x) is -4csc^2(x)cot(x)