What is the derivative of f(x)=3e^{-2x}ln(x) ?

The derivative of f(x)=3e^{-2x}ln(x) is 3(-2e^{-2x}ln(x)+(e^{-2x})/x)

What is the first derivative of f(x)=3e^{-2x}ln(x) ?

The first derivative of f(x)=3e^{-2x}ln(x) is 3(-2e^{-2x}ln(x)+(e^{-2x})/x)

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derivative of

f (x) = 3 e^{- 2 x} ln (x)

3 (- 2 e^{- 2 x} ln (x) + \frac{e ^{- 2 x}}{x})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{- 2 x}, g = ln (x)

= 3 (\frac{d}{d x} (e^{- 2 x}) ln (x) + \frac{d}{d x} (ln (x)) e^{- 2 x})

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 3 ((- 2 e^{- 2 x}) ln (x) + \frac{1}{x} e^{- 2 x})

Simplify

3 ((- 2 e^{- 2 x}) ln (x) + \frac{1}{x} e^{- 2 x}) : 3 (- 2 e^{- 2 x} ln (x) + \frac{e ^{- 2 x}}{x})

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

\frac{d}{d x} (arcsin (5 x^{3}))

\frac{d}{d x} (ln ∣ csc (3 x) ∣)

\int 4 e^{- 0.4 x} d x

\frac{∣ x ∣}{5 - x ^{2}}

What is the derivative of f(x)=3e^{-2x}ln(x) ?
The derivative of f(x)=3e^{-2x}ln(x) is 3(-2e^{-2x}ln(x)+(e^{-2x})/x)
What is the first derivative of f(x)=3e^{-2x}ln(x) ?
The first derivative of f(x)=3e^{-2x}ln(x) is 3(-2e^{-2x}ln(x)+(e^{-2x})/x)