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Popular >

derivative of (2-x)/(e^{3x)}

Solution

derivative of

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

Solution

- \frac{- 3 x + 7}{e ^{3 x}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 - x ) e ^{3 x} - \frac{d}{d x} ( e ^{3 x} ) ( 2 - x )}{( e ^{3 x} ) ^{2}}

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= \frac{( - 1 ) e ^{3 x} - e ^{3 x} \cdot 3 ( 2 - x )}{( e ^{3 x} ) ^{2}}

Simplify

\frac{( - 1 ) e ^{3 x} - e ^{3 x} \cdot 3 ( 2 - x )}{( e ^{3 x} ) ^{2}} : - \frac{- 3 x + 7}{e ^{3 x}}

= - \frac{- 3 x + 7}{e ^{3 x}}

Popular Examples

integral of (x^2)/((x+2)^3)

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

(dy)/(dx)=(8+x)^2

\frac{d y}{d x} = (8 + x)^{2}

integral of (3x^2-x+4)/(x^3+2x^2+6x)

\int \frac{3 x ^{2} - x + 4}{x ^{3} + 2 x ^{2} + 6 x} d x

derivative of (13/(ln(x)))

\frac{d}{d x} (\frac{13}{ln ( x )})

limit as x approaches infinity of (e^{2x}+e^x)/(e^{2x)-1}1

x \to \infty lim (\frac{e ^{2 x} + e ^{x}}{e ^{2 x} - 1} 1)

Frequently Asked Questions (FAQ)

What is the derivative of (2-x)/(e^{3x)} ?
The derivative of (2-x)/(e^{3x)} is -(-3x+7)/(e^{3x)}
What is the first derivative of (2-x)/(e^{3x)} ?
The first derivative of (2-x)/(e^{3x)} is -(-3x+7)/(e^{3x)}