What is the derivative of f(x)=(e^x)/(9x^2+2) ?

The derivative of f(x)=(e^x)/(9x^2+2) is (e^x(9x^2+2)-18xe^x)/((9x^2+2)^2)

What is the first derivative of f(x)=(e^x)/(9x^2+2) ?

The first derivative of f(x)=(e^x)/(9x^2+2) is (e^x(9x^2+2)-18xe^x)/((9x^2+2)^2)

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derivative of

f (x) = \frac{e ^{x}}{9 x ^{2} + 2}

\frac{e ^{x} ( 9 x ^{2} + 2 ) - 18 x e ^{x}}{( 9 x ^{2} + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{9 x ^{2} + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 9 x ^{2} + 2 ) - \frac{d}{d x} ( 9 x ^{2} + 2 ) e ^{x}}{( 9 x ^{2} + 2 ) ^{2}}

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

\frac{d}{d x} (9 x^{2} + 2) = 18 x

= \frac{e ^{x} ( 9 x ^{2} + 2 ) - 18 x e ^{x}}{( 9 x ^{2} + 2 ) ^{2}}

\int \frac{1}{u ^{2}} d u

\int 4 e^{- 3 x} d x

\frac{d}{d x} (x^{\frac{1}{8}})

f (x) = \frac{x}{6}

f (x) = \frac{6 x ^{2} - 1}{- 3 x + 1}, at x = 0

What is the derivative of f(x)=(e^x)/(9x^2+2) ?
The derivative of f(x)=(e^x)/(9x^2+2) is (e^x(9x^2+2)-18xe^x)/((9x^2+2)^2)
What is the first derivative of f(x)=(e^x)/(9x^2+2) ?
The first derivative of f(x)=(e^x)/(9x^2+2) is (e^x(9x^2+2)-18xe^x)/((9x^2+2)^2)