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Popular Calculus >

derivative of acsc^2(kx)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

a \cdot 2 csc (k x) (- cot (k x) csc (k x) k) : - 2 ak csc^{2} (k x) cot (k x)

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

Graph

Popular Examples

derivative of (6x+5(x^3-2))

\frac{d}{d x} ((6 x + 5) (x^{3} - 2))

derivative of e^{e^{e^{e^x}}}

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

integral of r^2

\int r^{2} d r

limit as x approaches 0 of (7x)/(cot(x))

x \to 0 lim (\frac{7 x}{cot ( x )})

(\partial)/(\partial s)(ssin(t))

\frac{\partial}{\partial s} (s sin (t))

Frequently Asked Questions (FAQ)

What is the derivative of acsc^2(kx) ?
The derivative of acsc^2(kx) is -2akcsc^2(kx)cot(kx)
What is the first derivative of acsc^2(kx) ?
The first derivative of acsc^2(kx) is -2akcsc^2(kx)cot(kx)