What is the derivative of 3e^{-5x}ln(x) ?

The derivative of 3e^{-5x}ln(x) is 3(-5e^{-5x}ln(x)+(e^{-5x})/x)

What is the first derivative of 3e^{-5x}ln(x) ?

The first derivative of 3e^{-5x}ln(x) is 3(-5e^{-5x}ln(x)+(e^{-5x})/x)

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\frac{d}{d x} (3 e^{- 5 x} ln (x))

3 (- 5 e^{- 5 x} ln (x) + \frac{e ^{- 5 x}}{x})

Solution steps

\frac{d}{d x} (3 e^{- 5 x} ln (x))

Take the constant out:

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

= 3 \frac{d}{d x} (e^{- 5 x} ln (x))

Apply the Product Rule:

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

f = e^{- 5 x}, g = ln (x)

= 3 (\frac{d}{d x} (e^{- 5 x}) ln (x) + \frac{d}{d x} (ln (x)) e^{- 5 x})

\frac{d}{d x} (e^{- 5 x}) = - 5 e^{- 5 x}

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

= 3 ((- 5 e^{- 5 x}) ln (x) + \frac{1}{x} e^{- 5 x})

Simplify

3 ((- 5 e^{- 5 x}) ln (x) + \frac{1}{x} e^{- 5 x}) : 3 (- 5 e^{- 5 x} ln (x) + \frac{e ^{- 5 x}}{x})

= 3 (- 5 e^{- 5 x} ln (x) + \frac{e ^{- 5 x}}{x})

ln (sin (8 x))

\frac{d ^{2}}{d x ^{2}} (a x^{2} + b x + c)

x \to \infty lim (0. 4^{x})

\frac{d}{d a} (tan (a) csc (a))

g (t) = 1 + ln (t)

What is the derivative of 3e^{-5x}ln(x) ?
The derivative of 3e^{-5x}ln(x) is 3(-5e^{-5x}ln(x)+(e^{-5x})/x)
What is the first derivative of 3e^{-5x}ln(x) ?
The first derivative of 3e^{-5x}ln(x) is 3(-5e^{-5x}ln(x)+(e^{-5x})/x)