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Popular Calculus >

derivative of e^{arccsc(x})

Solution

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

Solution

- \frac{e ^{arccsc (x)}}{x x ^{2} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{arccsc (x)} (- \frac{1}{x ^{2} x ^{2} - 1})

Simplify

e^{arccsc (x)} (- \frac{1}{x ^{2} x ^{2} - 1}) : - \frac{e ^{arccsc (x)}}{x x ^{2} - 1}

= - \frac{e ^{arccsc (x)}}{x x ^{2} - 1}

Graph

Popular Examples

f (x) = 4 x

(\partial)/(\partial x)(-15(3x+y)^4)

\frac{\partial}{\partial x} (- 15 (3 x + y)^{4})

y^{^{'}} = (y - 1)^{2}

derivative of-(4x/((x^2-4)^2))

\frac{d}{d x} (- \frac{4 x}{( x ^{2} - 4 ) ^{2}})

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

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

Frequently Asked Questions (FAQ)

What is the derivative of e^{arccsc(x}) ?
The derivative of e^{arccsc(x}) is -(e^{arccsc(x)})/(xsqrt(x^2-1))
What is the first derivative of e^{arccsc(x}) ?
The first derivative of e^{arccsc(x}) is -(e^{arccsc(x)})/(xsqrt(x^2-1))