What is the derivative of ((x^2)/(e^{2x)})^6 ?

The derivative of ((x^2)/(e^{2x)})^6 is (12x^{11}(1-x))/(e^{12x)}

What is the first derivative of ((x^2)/(e^{2x)})^6 ?

The first derivative of ((x^2)/(e^{2x)})^6 is (12x^{11}(1-x))/(e^{12x)}

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derivative of

(\frac{x ^{2}}{e ^{2 x}})^{6}

\frac{12 x ^{11} ( 1 - x )}{e ^{12 x}}

Solution steps

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

Apply the chain rule:

6 (\frac{x ^{2}}{e ^{2 x}})^{5} \frac{d}{d x} (\frac{x ^{2}}{e ^{2 x}})

= 6 (\frac{x ^{2}}{e ^{2 x}})^{5} \frac{d}{d x} (\frac{x ^{2}}{e ^{2 x}})

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

= 6 (\frac{x ^{2}}{e ^{2 x}})^{5} \frac{2 x ( 1 - x )}{e ^{2 x}}

Simplify

6 (\frac{x ^{2}}{e ^{2 x}})^{5} \frac{2 x ( 1 - x )}{e ^{2 x}} : \frac{12 x ^{11} ( 1 - x )}{e ^{12 x}}

= \frac{12 x ^{11} ( 1 - x )}{e ^{12 x}}

- 7 x + \frac{3}{x ^{6}}

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

\frac{d}{d x} (f (x) - 4 x + 1)

n = 1 \sum \infty (\frac{10}{11})^{n}

f (x) = - x - \frac{1}{x}

What is the derivative of ((x^2)/(e^{2x)})^6 ?
The derivative of ((x^2)/(e^{2x)})^6 is (12x^{11}(1-x))/(e^{12x)}
What is the first derivative of ((x^2)/(e^{2x)})^6 ?
The first derivative of ((x^2)/(e^{2x)})^6 is (12x^{11}(1-x))/(e^{12x)}