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Popular >

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}

Popular Examples

derivative of-asin(x+bcos(x))

\frac{d}{d x} (- a sin (x) + b cos (x))

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 1/(sqrt(x)(x^2-2/x))

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

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))