What is the derivative of ((x+3)^2)/(e^x) ?

The derivative of ((x+3)^2)/(e^x) is ((3+x)(-x-1))/(e^x)

What is the first derivative of ((x+3)^2)/(e^x) ?

The first derivative of ((x+3)^2)/(e^x) is ((3+x)(-x-1))/(e^x)

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derivative of

\frac{( x + 3 ) ^{2}}{e ^{x}}

\frac{( 3 + x ) ( - x - 1 )}{e ^{x}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y = (x^{2} + x + 8)

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

\frac{( 2 x + 1 )}{( x + 1 )}

\frac{tanh ( 4 x + 1 )}{5}

\frac{d}{d x} \frac{1}{( x + { n } ) \cdot x}

What is the derivative of ((x+3)^2)/(e^x) ?
The derivative of ((x+3)^2)/(e^x) is ((3+x)(-x-1))/(e^x)
What is the first derivative of ((x+3)^2)/(e^x) ?
The first derivative of ((x+3)^2)/(e^x) is ((3+x)(-x-1))/(e^x)