What is the derivative of (6x)/(e^x) ?

The derivative of (6x)/(e^x) is (6(1-x))/(e^x)

What is the first derivative of (6x)/(e^x) ?

The first derivative of (6x)/(e^x) is (6(1-x))/(e^x)

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derivative of

\frac{6 x}{e ^{x}}

\frac{6 ( 1 - x )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{6 x}{e ^{x}})

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d x}{d x} e ^{x} - \frac{d}{d x} ( e ^{x} ) x}{( e ^{x} ) ^{2}}

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

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

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

Simplify

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

= \frac{6 ( 1 - x )}{e ^{x}}

x y^{^{'}} + 6 y = - 35 x cos (x^{7})

\int x^{3} 12 + x^{4} d x

n = 1 \sum \infty (- 1)^{n}

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

\int (x - 8)^{\frac{3}{2}} d x

What is the derivative of (6x)/(e^x) ?
The derivative of (6x)/(e^x) is (6(1-x))/(e^x)
What is the first derivative of (6x)/(e^x) ?
The first derivative of (6x)/(e^x) is (6(1-x))/(e^x)