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Popular >

derivative of (e^x)/(6x^2+7)

Solution

derivative of

\frac{e ^{x}}{6 x ^{2} + 7}

Solution

\frac{e ^{x} ( 6 x ^{2} + 7 ) - 12 x e ^{x}}{( 6 x ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{6 x ^{2} + 7})

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} + 7 ) - \frac{d}{d x} ( 6 x ^{2} + 7 ) e ^{x}}{( 6 x ^{2} + 7 ) ^{2}}

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

\frac{d}{d x} (6 x^{2} + 7) = 12 x

= \frac{e ^{x} ( 6 x ^{2} + 7 ) - 12 x e ^{x}}{( 6 x ^{2} + 7 ) ^{2}}

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\int 8 x^{\frac{1}{3}} d x

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x \to 0 - lim (\frac{x ^{2} - x}{∣ x ∣})

Frequently Asked Questions (FAQ)

What is the derivative of (e^x)/(6x^2+7) ?
The derivative of (e^x)/(6x^2+7) is (e^x(6x^2+7)-12xe^x)/((6x^2+7)^2)
What is the first derivative of (e^x)/(6x^2+7) ?
The first derivative of (e^x)/(6x^2+7) is (e^x(6x^2+7)-12xe^x)/((6x^2+7)^2)