What is the derivative of (e^x/(6x^2+5)) ?

The derivative of (e^x/(6x^2+5)) is (e^x(6x^2+5)-12xe^x)/((6x^2+5)^2)

What is the first derivative of (e^x/(6x^2+5)) ?

The first derivative of (e^x/(6x^2+5)) is (e^x(6x^2+5)-12xe^x)/((6x^2+5)^2)

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

\frac{e ^{x} ( 6 x ^{2} + 5 ) - 12 x e ^{x}}{( 6 x ^{2} + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (6 x^{2} + 5) = 12 x

= \frac{e ^{x} ( 6 x ^{2} + 5 ) - 12 x e ^{x}}{( 6 x ^{2} + 5 ) ^{2}}

What is the derivative of (e^x/(6x^2+5)) ?
The derivative of (e^x/(6x^2+5)) is (e^x(6x^2+5)-12xe^x)/((6x^2+5)^2)
What is the first derivative of (e^x/(6x^2+5)) ?
The first derivative of (e^x/(6x^2+5)) is (e^x(6x^2+5)-12xe^x)/((6x^2+5)^2)