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Popular >

derivative of e^{(-x/3})

Solution

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

Solution

- \frac{1}{3} e^{- \frac{x}{3}}

Solution steps

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

Simplify

e^{\frac{- x}{3}} : e^{- \frac{x}{3}}

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x}{3}) = - \frac{1}{3}

= e^{- \frac{x}{3}} (- \frac{1}{3})

Simplify

= - \frac{1}{3} e^{- \frac{x}{3}}

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integral of e^{2θ}cos(3θ)

\int e^{2 θ} cos (3 θ) d θ

derivative of y=2x^2-12x+6 derivative of

y = 2 x^{2} - 12 x + 6

integral of 1/(x-x^2)

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

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\frac{d}{d x} (π \cdot x^{2})

derivative of y=((3x^5+9))/(x^3)derivative of

y = \frac{( 3 x ^{5} + 9 )}{x ^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of e^{(-x/3}) ?
The derivative of e^{(-x/3}) is -1/3 e^{-x/3}
What is the first derivative of e^{(-x/3}) ?
The first derivative of e^{(-x/3}) is -1/3 e^{-x/3}