What is the derivative of f(x)=(x+2)e^{1/x} ?

The derivative of f(x)=(x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)

What is the first derivative of f(x)=(x+2)e^{1/x} ?

The first derivative of f(x)=(x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)

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derivative of

f (x) = (x + 2) e^{\frac{1}{x}}

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 2, g = e^{\frac{1}{x}}

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

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

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

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

Simplify

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

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

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

y^{^{'}} = e^{y - x}

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

\frac{sec ( x )}{1 + sec ( x )}

\int x ln^{3} (x) d x

What is the derivative of f(x)=(x+2)e^{1/x} ?
The derivative of f(x)=(x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)
What is the first derivative of f(x)=(x+2)e^{1/x} ?
The first derivative of f(x)=(x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)