What is the derivative of (e^x)/(8x^2+1) ?

The derivative of (e^x)/(8x^2+1) is (e^x(8x^2+1)-16xe^x)/((8x^2+1)^2)

What is the first derivative of (e^x)/(8x^2+1) ?

The first derivative of (e^x)/(8x^2+1) is (e^x(8x^2+1)-16xe^x)/((8x^2+1)^2)

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derivative of

\frac{e ^{x}}{8 x ^{2} + 1}

\frac{e ^{x} ( 8 x ^{2} + 1 ) - 16 x e ^{x}}{( 8 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{8 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} ) ( 8 x ^{2} + 1 ) - \frac{d}{d x} ( 8 x ^{2} + 1 ) e ^{x}}{( 8 x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (8 x^{2} + 1) = 16 x

= \frac{e ^{x} ( 8 x ^{2} + 1 ) - 16 x e ^{x}}{( 8 x ^{2} + 1 ) ^{2}}

\int \frac{x}{( 2 + x ^{\frac{3}{2}} ) ^{3}} d x

\int_{1}^{4} 5 - x d x

\int_{0}^{4} \frac{1}{64 - x ^{2}} d x

\frac{\partial}{\partial x} (5 x y e^{- x^{2} - y^{2}})

e^{1}

What is the derivative of (e^x)/(8x^2+1) ?
The derivative of (e^x)/(8x^2+1) is (e^x(8x^2+1)-16xe^x)/((8x^2+1)^2)
What is the first derivative of (e^x)/(8x^2+1) ?
The first derivative of (e^x)/(8x^2+1) is (e^x(8x^2+1)-16xe^x)/((8x^2+1)^2)