What is the derivative of (e^{x^2-1})/(2sqrt(x)) ?

The derivative of (e^{x^2-1})/(2sqrt(x)) is (4e^{x^2-1}x^2-e^{x^2-1})/(4xsqrt(x))

What is the first derivative of (e^{x^2-1})/(2sqrt(x)) ?

The first derivative of (e^{x^2-1})/(2sqrt(x)) is (4e^{x^2-1}x^2-e^{x^2-1})/(4xsqrt(x))

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derivative of

\frac{e ^{x^{2} - 1}}{2 x}

\frac{4 e ^{x^{2} - 1} x ^{2} - e ^{x^{2} - 1}}{4 x x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{1}{2} \cdot \frac{e ^{x^{2} - 1} \cdot 2 x x - \frac{1}{2 x} e ^{x^{2} - 1}}{( x ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{e ^{x^{2} - 1} \cdot 2 x x - \frac{1}{2 x} e ^{x^{2} - 1}}{( x ) ^{2}} : \frac{4 e ^{x^{2} - 1} x ^{2} - e ^{x^{2} - 1}}{4 x x}

= \frac{4 e ^{x^{2} - 1} x ^{2} - e ^{x^{2} - 1}}{4 x x}

What is the derivative of (e^{x^2-1})/(2sqrt(x)) ?
The derivative of (e^{x^2-1})/(2sqrt(x)) is (4e^{x^2-1}x^2-e^{x^2-1})/(4xsqrt(x))
What is the first derivative of (e^{x^2-1})/(2sqrt(x)) ?
The first derivative of (e^{x^2-1})/(2sqrt(x)) is (4e^{x^2-1}x^2-e^{x^2-1})/(4xsqrt(x))