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Popular >

derivative of ((e^{-x}))/x

Solution

derivative of

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

Solution

\frac{- e ^{- x} x - e ^{- x}}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

= \frac{- e ^{- x} x - e ^{- x}}{x ^{2}}

Popular Examples

derivative of cos(arccos(ax^2+bx+c))

\frac{d}{d x} (cos (arccos (a x^{2} + b x + c)))

(\partial)/(\partial x)((e^x-4x)sin(y))

\frac{\partial}{\partial x} ((e^{x} - 4 x) sin (y))

tangent of y=(x-2)(x^2+4),(1,-5)tangent of

y = (x - 2) (x^{2} + 4), (1, - 5)

derivative of ln(2)derivative of

ln (2)

(dy)/(dx)= y/(x+1)+4x^2+4x

\frac{d y}{d x} = \frac{y}{x + 1} + 4 x^{2} + 4 x

Frequently Asked Questions (FAQ)

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