Solve d/dx ( 1/(2 sqrt(x)) e^(x) ln x e^(x)/x )

Question

Evaluate the derivative

\frac{4 x e ^{2 x} ln ( x ) \times x + 2 e ^{2 x} x - 3 e ^{2 x} ln ( x ) \times x}{4 x ^{3}}

Evaluate

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

Multiply the terms

More Steps

\frac{d}{d x} (\frac{e ^{2 x} ln ( x )}{2 x \times x})

Use differentiation rule \frac{d}{d x} (\frac{f ( x )}{g ( x )}) = \frac{\frac{d}{d x} ( f ( x )) \times g ( x ) - f ( x ) \times \frac{d}{d x} ( g ( x ) )}{( g ( x ) ) ^{2}}

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

Calculate

More Steps

\frac{\frac{2 e ^{2 x} l n ( x ) \times x + e ^{2 x}}{x} \times 2 x \times x - e ^{2 x} ln ( x ) \times \frac{d}{d x} ( 2 x \times x )}{( 2 x \times x ) ^{2}}

Calculate

More Steps

\frac{\frac{2 e ^{2 x} l n ( x ) \times x + e ^{2 x}}{x} \times 2 x \times x - e ^{2 x} ln ( x ) \times 3 x}{( 2 x \times x ) ^{2}}

Multiply the terms

More Steps

\frac{4 x e ^{2 x} ln ( x ) \times x + 2 e ^{2 x} x - e ^{2 x} ln ( x ) \times 3 x}{( 2 x \times x ) ^{2}}

Use the commutative property to reorder the terms

\frac{4 x e ^{2 x} ln ( x ) \times x + 2 e ^{2 x} x - 3 e ^{2 x} ln ( x ) \times x}{( 2 x \times x ) ^{2}}

Solution

More Steps

\frac{4 x e ^{2 x} ln ( x ) \times x + 2 e ^{2 x} x - 3 e ^{2 x} ln ( x ) \times x}{4 x ^{3}}

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