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Popular >

derivative of-(e^x/x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= - \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

(dy)/(dx)= 2/3 (x^2+1)^{3/2}

\frac{d y}{d x} = \frac{2}{3} (x^{2} + 1)^{\frac{3}{2}}

derivative of 5/(x^9)

\frac{d}{d x} (\frac{5}{x ^{9}})

integral from-4 to 4 of sqrt(16-x^2)

\int_{- 4}^{4} 16 - x^{2} d x

integral of e^{0.2t}

\int e^{0.2 t} d t

integral of (3x-9)/((x^2+2x+4)^2)

\int \frac{3 x - 9}{( x ^{2} + 2 x + 4 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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