What is the derivative of (e^x)/(3x^2+7) ?

The derivative of (e^x)/(3x^2+7) is (e^x(3x^2+7)-6xe^x)/((3x^2+7)^2)

What is the first derivative of (e^x)/(3x^2+7) ?

The first derivative of (e^x)/(3x^2+7) is (e^x(3x^2+7)-6xe^x)/((3x^2+7)^2)

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derivative of

\frac{e ^{x}}{3 x ^{2} + 7}

\frac{e ^{x} ( 3 x ^{2} + 7 ) - 6 x e ^{x}}{( 3 x ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{3 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} ) ( 3 x ^{2} + 7 ) - \frac{d}{d x} ( 3 x ^{2} + 7 ) e ^{x}}{( 3 x ^{2} + 7 ) ^{2}}

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

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= \frac{e ^{x} ( 3 x ^{2} + 7 ) - 6 x e ^{x}}{( 3 x ^{2} + 7 ) ^{2}}

\int 5 + x d x

\int x - 5 d x

\int \frac{17}{( x ^{2} - 1 ) ^{2}} d x

x \to 1 lim ((1 - \frac{5}{x})^{x})

(8 x + 5) (x^{2} - 3 x)

What is the derivative of (e^x)/(3x^2+7) ?
The derivative of (e^x)/(3x^2+7) is (e^x(3x^2+7)-6xe^x)/((3x^2+7)^2)
What is the first derivative of (e^x)/(3x^2+7) ?
The first derivative of (e^x)/(3x^2+7) is (e^x(3x^2+7)-6xe^x)/((3x^2+7)^2)