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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{4} + x ^{2} + 25}{5 x ^{4} ( x ^{2} + 25 )} d x

\frac{\partial}{\partial x} (2 x y (x + y) + x^{2} + 2 x)

\frac{\partial}{\partial y} (ln (x^{2} y))

7 \cdot ln (x)

sin^{3} (3 x)

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