What is the derivative of (x^2/(e^{3-4x)}) ?

The derivative of (x^2/(e^{3-4x)}) is 2e^{4x-3}x(1+2x)

What is the first derivative of (x^2/(e^{3-4x)}) ?

The first derivative of (x^2/(e^{3-4x)}) is 2e^{4x-3}x(1+2x)

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\frac{d}{d x} (\frac{x ^{2}}{e ^{3 - 4 x}})

2 e^{4 x - 3} x (1 + 2 x)

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{e ^{3 - 4 x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) e ^{3 - 4 x} - \frac{d}{d x} ( e ^{3 - 4 x} ) x ^{2}}{( e ^{3 - 4 x} ) ^{2}}

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

\frac{d}{d x} (e^{3 - 4 x}) = - 4 e^{3 - 4 x}

= \frac{2 x e ^{3 - 4 x} - ( - 4 e ^{3 - 4 x} ) x ^{2}}{( e ^{3 - 4 x} ) ^{2}}

Simplify

\frac{2 x e ^{3 - 4 x} - ( - 4 e ^{3 - 4 x} ) x ^{2}}{( e ^{3 - 4 x} ) ^{2}} : 2 e^{4 x - 3} x (1 + 2 x)

= 2 e^{4 x - 3} x (1 + 2 x)

What is the derivative of (x^2/(e^{3-4x)}) ?
The derivative of (x^2/(e^{3-4x)}) is 2e^{4x-3}x(1+2x)
What is the first derivative of (x^2/(e^{3-4x)}) ?
The first derivative of (x^2/(e^{3-4x)}) is 2e^{4x-3}x(1+2x)