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Popular >

derivative of (e^x/x+ln(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

integral of u/(1-u^2)

\int \frac{u}{1 - u ^{2}} d u

derivative of (csc^3(x)/(ln(x^2)))

\frac{d}{d x} (\frac{csc ^{3} ( x )}{ln ( x ^{2} )})

(\partial)/(\partial x)(y^2sin(4x))

\frac{\partial}{\partial x} (y^{2} sin (4 x))

derivative of 2ln(4x)

\frac{d}{d x} (2 ln (4 x))

derivative of rx+s

\frac{d}{d x} (r x + s)

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/x+ln(x)) ?
The derivative of (e^x/x+ln(x)) is (e^xx-e^x)/(x^2)+1/x
What is the first derivative of (e^x/x+ln(x)) ?
The first derivative of (e^x/x+ln(x)) is (e^xx-e^x)/(x^2)+1/x