What is the derivative of f(x)=-3/(e^{3x)} ?

The derivative of f(x)=-3/(e^{3x)} is 9e^{-3x}

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

The first derivative of f(x)=-3/(e^{3x)} is 9e^{-3x}

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derivative of

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

9 e^{- 3 x}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= - 3 e^{- 3 x} (- 3)

Simplify

= 9 e^{- 3 x}

x \to - 3 lim (x^{2} + 4 x + 1)

\int \frac{1}{x ( 4 - x )} d x

\frac{\partial}{\partial y} (y e^{2 x y} + x)

\int X d X

\int \frac{x}{2 x ^{2} + 3} d x

What is the derivative of f(x)=-3/(e^{3x)} ?
The derivative of f(x)=-3/(e^{3x)} is 9e^{-3x}
What is the first derivative of f(x)=-3/(e^{3x)} ?
The first derivative of f(x)=-3/(e^{3x)} is 9e^{-3x}