What is the derivative of f(x)=((e^x))/(7x^2+1) ?

The derivative of f(x)=((e^x))/(7x^2+1) is (e^x(7x^2+1)-14xe^x)/((7x^2+1)^2)

What is the first derivative of f(x)=((e^x))/(7x^2+1) ?

The first derivative of f(x)=((e^x))/(7x^2+1) is (e^x(7x^2+1)-14xe^x)/((7x^2+1)^2)

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derivative of

f (x) = \frac{( e ^{x} )}{7 x ^{2} + 1}

\frac{e ^{x} ( 7 x ^{2} + 1 ) - 14 x e ^{x}}{( 7 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 7 x ^{2} + 1 ) - \frac{d}{d x} ( 7 x ^{2} + 1 ) e ^{x}}{( 7 x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= \frac{e ^{x} ( 7 x ^{2} + 1 ) - 14 x e ^{x}}{( 7 x ^{2} + 1 ) ^{2}}

\int x^{3} 2 x^{4} + 3 d x

\frac{\partial}{\partial r} (r ln (r^{2} + s^{2}))

\int (3 x^{2} - 8 x) d x

\int \frac{2 + x}{x} d x

x \to 1 - lim (x + 1)

What is the derivative of f(x)=((e^x))/(7x^2+1) ?
The derivative of f(x)=((e^x))/(7x^2+1) is (e^x(7x^2+1)-14xe^x)/((7x^2+1)^2)
What is the first derivative of f(x)=((e^x))/(7x^2+1) ?
The first derivative of f(x)=((e^x))/(7x^2+1) is (e^x(7x^2+1)-14xe^x)/((7x^2+1)^2)