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Popular >

derivative of f(x)=e^{-x}-e^{-x}x

Solution

derivative of

f (x) = e^{- x} - e^{- x} x

Solution

e^{- x} x - 2 e^{- x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - e^{- x} - (- e^{- x} x + e^{- x})

Simplify

= e^{- x} x - 2 e^{- x}

Popular Examples

derivative of arcsin(cos(x))

\frac{d}{d x} (arcsin (cos (x)))

inverse oflaplace (s+1)/(s(s-1)^2)inverse laplace

\frac{s + 1}{s ( s - 1 ) ^{2}}

(\partial)/(\partial x)(e^{-(x+y)})

\frac{\partial}{\partial x} (e^{- (x + y)})

(t^2-1)y^'+2ty^2=0

(t^{2} - 1) y^{^{'}} + 2 t y^{2} = 0

integral of (t^2)/((a+bt^3)^2)

\int \frac{t ^{2}}{( a + b t ^{3} ) ^{2}} d t

Frequently Asked Questions (FAQ)

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