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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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