What is the derivative of f(x)=6e^{-1/6 x^2} ?

The derivative of f(x)=6e^{-1/6 x^2} is -2e^{-(x^2)/6}x

What is the first derivative of f(x)=6e^{-1/6 x^2} ?

The first derivative of f(x)=6e^{-1/6 x^2} is -2e^{-(x^2)/6}x

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derivative of

f (x) = 6 e^{- \frac{1}{6} x^{2}}

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

Solution steps

\frac{d}{d x} (6 e^{- \frac{1}{6} x^{2}})

Simplify

6 e^{- \frac{1}{6} x^{2}} : 6 e^{- \frac{x ^{2}}{6}}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x ^{2}}{6}) = - \frac{x}{3}

= 6 e^{- \frac{x ^{2}}{6}} (- \frac{x}{3})

Simplify

6 e^{- \frac{x ^{2}}{6}} (- \frac{x}{3}) : - 2 e^{- \frac{x ^{2}}{6}} x

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

\int 24 y (1 - x - y) d y

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

\frac{d}{d x} (\frac{( 3 x + 1 )}{x ^{\frac{2}{3}}})

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

\int t e^{- 2 t} d t

What is the derivative of f(x)=6e^{-1/6 x^2} ?
The derivative of f(x)=6e^{-1/6 x^2} is -2e^{-(x^2)/6}x
What is the first derivative of f(x)=6e^{-1/6 x^2} ?
The first derivative of f(x)=6e^{-1/6 x^2} is -2e^{-(x^2)/6}x