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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{3 x} ) ( 1 - x ^{2} ) - \frac{d}{d x} ( 1 - x ^{2} ) e ^{3 x}}{( 1 - x ^{2} ) ^{2}}

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

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

= \frac{e ^{3 x} \cdot 3 ( 1 - x ^{2} ) - ( - 2 x ) e ^{3 x}}{( 1 - x ^{2} ) ^{2}}

Simplify

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

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