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Popular >

derivative of (e^{6x}/x)

Solution

\frac{d}{d x} (\frac{e ^{6 x}}{x})

Solution

\frac{6 e ^{6 x} x - e ^{6 x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{6 x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{6 x} ) x - \frac{d x}{d x} e ^{6 x}}{x ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

= \frac{e ^{6 x} \cdot 6 x - 1 \cdot e ^{6 x}}{x ^{2}}

Simplify

= \frac{6 e ^{6 x} x - e ^{6 x}}{x ^{2}}

Popular Examples

limit as x approaches 3 of x+3

x \to 3 lim (x + 3)

derivative of-(18)/(x^3)derivative of

- \frac{18}{x ^{3}}

(dy)/(dx)=(xy+y^2+x^2)/(x^2)

\frac{d y}{d x} = \frac{x y + y ^{2} + x ^{2}}{x ^{2}}

integral from-1 to 3 of |x-2x^2|

\int_{- 1}^{3} x - 2 x^{2} d x

integral of ((e^{2x}))/(1+e^{4x)}

\int \frac{( e ^{2 x} )}{1 + e ^{4 x}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (e^{6x}/x) ?
The derivative of (e^{6x}/x) is (6e^{6x}x-e^{6x})/(x^2)
What is the first derivative of (e^{6x}/x) ?
The first derivative of (e^{6x}/x) is (6e^{6x}x-e^{6x})/(x^2)