What is the derivative of (e^x)/(-8x^7) ?

The derivative of (e^x)/(-8x^7) is -(e^x(x-7))/(8x^8)

What is the first derivative of (e^x)/(-8x^7) ?

The first derivative of (e^x)/(-8x^7) is -(e^x(x-7))/(8x^8)

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derivative of

\frac{e ^{x}}{- 8 x ^{7}}

- \frac{e ^{x} ( x - 7 )}{8 x ^{8}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{- 8 x ^{7}})

Simplify

\frac{e ^{x}}{- 8 x ^{7}} : - \frac{e ^{x}}{8 x ^{7}}

= \frac{d}{d x} (- \frac{e ^{x}}{8 x ^{7}})

Take the constant out:

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

= - \frac{1}{8} \frac{d}{d x} (\frac{e ^{x}}{x ^{7}})

Apply the Quotient Rule:

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

= - \frac{1}{8} \cdot \frac{\frac{d}{d x} ( e ^{x} ) x ^{7} - \frac{d}{d x} ( x ^{7} ) e ^{x}}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= - \frac{1}{8} \cdot \frac{e ^{x} x ^{7} - 7 x ^{6} e ^{x}}{( x ^{7} ) ^{2}}

Simplify

- \frac{1}{8} \cdot \frac{e ^{x} x ^{7} - 7 x ^{6} e ^{x}}{( x ^{7} ) ^{2}} : - \frac{e ^{x} ( x - 7 )}{8 x ^{8}}

= - \frac{e ^{x} ( x - 7 )}{8 x ^{8}}

What is the derivative of (e^x)/(-8x^7) ?
The derivative of (e^x)/(-8x^7) is -(e^x(x-7))/(8x^8)
What is the first derivative of (e^x)/(-8x^7) ?
The first derivative of (e^x)/(-8x^7) is -(e^x(x-7))/(8x^8)