What is the derivative of x/(e^x-100x) ?

The derivative of x/(e^x-100x) is (-e^xx+e^x)/((e^x-100x)^2)

What is the first derivative of x/(e^x-100x) ?

The first derivative of x/(e^x-100x) is (-e^xx+e^x)/((e^x-100x)^2)

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\frac{d}{d x} (\frac{x}{e ^{x} - 100 x})

\frac{- e ^{x} x + e ^{x}}{( e ^{x} - 100 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{e ^{x} - 100 x})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( e ^{x} - 100 x ) - \frac{d}{d x} ( e ^{x} - 100 x ) x}{( e ^{x} - 100 x ) ^{2}}

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

\frac{d}{d x} (e^{x} - 100 x) = e^{x} - 100

= \frac{1 \cdot ( e ^{x} - 100 x ) - ( e ^{x} - 100 ) x}{( e ^{x} - 100 x ) ^{2}}

Simplify

\frac{1 \cdot ( e ^{x} - 100 x ) - ( e ^{x} - 100 ) x}{( e ^{x} - 100 x ) ^{2}} : \frac{- e ^{x} x + e ^{x}}{( e ^{x} - 100 x ) ^{2}}

= \frac{- e ^{x} x + e ^{x}}{( e ^{x} - 100 x ) ^{2}}

r

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

\int \frac{32}{32 + e ^{x}} d x

x^{\frac{3}{2}}

x \to 7 lim (2 - x - 3)

What is the derivative of x/(e^x-100x) ?
The derivative of x/(e^x-100x) is (-e^xx+e^x)/((e^x-100x)^2)
What is the first derivative of x/(e^x-100x) ?
The first derivative of x/(e^x-100x) is (-e^xx+e^x)/((e^x-100x)^2)