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Popular >

derivative of (e^{3x}/x)

Solution

\frac{d}{d x} (\frac{e ^{3 x}}{x})

Solution

\frac{3 e ^{3 x} x - e ^{3 x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{3 x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{3 x} ) x - \frac{d x}{d x} e ^{3 x}}{x ^{2}}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d x}{d x} = 1

= \frac{e ^{3 x} \cdot 3 x - 1 \cdot e ^{3 x}}{x ^{2}}

Simplify

= \frac{3 e ^{3 x} x - e ^{3 x}}{x ^{2}}

Popular Examples

derivative of ln(8-4x)

\frac{d}{d x} (ln (8 - 4 x))

derivative of cos(sqrt(x)+e^x)

\frac{d}{d x} (cos (x + e^{x}))

derivative of (x^2+4/(5x-9))

\frac{d}{d x} (\frac{x ^{2} + 4}{5 x - 9})

y^{''}-4y^'+3y=0,y(0)=-7.5,y^'(0)= 23/5

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = - 7.5, y^{^{'}} (0) = \frac{23}{5}

derivative of f(x)=sqrt(3)derivative of

f (x) = 3

Frequently Asked Questions (FAQ)

What is the derivative of (e^{3x}/x) ?
The derivative of (e^{3x}/x) is (3e^{3x}x-e^{3x})/(x^2)
What is the first derivative of (e^{3x}/x) ?
The first derivative of (e^{3x}/x) is (3e^{3x}x-e^{3x})/(x^2)