What is the derivative of 10000(12+xe^{-0.05x}) ?

The derivative of 10000(12+xe^{-0.05x}) is 10000(0.4e^{-0.05x}-0.05e^{-0.05x}x)

What is the first derivative of 10000(12+xe^{-0.05x}) ?

The first derivative of 10000(12+xe^{-0.05x}) is 10000(0.4e^{-0.05x}-0.05e^{-0.05x}x)

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\frac{d}{d x} (10000 (12 + x) e^{- 0.05 x})

10000 (0.4 e^{- 0.05 x} - 0.05 e^{- 0.05 x} x)

Solution steps

\frac{d}{d x} (10000 (12 + x) e^{- 0.05 x})

Take the constant out:

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

= 10000 \frac{d}{d x} ((12 + x) e^{- 0.05 x})

Apply the Product Rule:

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

f = 12 + x, g = e^{- 0.05 x}

= 10000 (\frac{d}{d x} (12 + x) e^{- 0.05 x} + \frac{d}{d x} (e^{- 0.05 x}) (12 + x))

\frac{d}{d x} (12 + x) = 1

\frac{d}{d x} (e^{- 0.05 x}) = - 0.05 e^{- 0.05 x}

= 10000 (1 \cdot e^{- 0.05 x} + (- 0.05 e^{- 0.05 x}) (12 + x))

Simplify

10000 (1 \cdot e^{- 0.05 x} + (- 0.05 e^{- 0.05 x}) (12 + x)) : 10000 (0.4 e^{- 0.05 x} - 0.05 e^{- 0.05 x} x)

= 10000 (0.4 e^{- 0.05 x} - 0.05 e^{- 0.05 x} x)

x \to 1 lim (\frac{4 x - 1}{x - 1})

\frac{1}{5} (9 x + 8)^{3}

f (x) = - 4 x^{2} - 5 x + 2

x \to 4 lim (\frac{x - 2}{x - 4})

\int_{0}^{π} x cos (3 x) d x

What is the derivative of 10000(12+xe^{-0.05x}) ?
The derivative of 10000(12+xe^{-0.05x}) is 10000(0.4e^{-0.05x}-0.05e^{-0.05x}x)
What is the first derivative of 10000(12+xe^{-0.05x}) ?
The first derivative of 10000(12+xe^{-0.05x}) is 10000(0.4e^{-0.05x}-0.05e^{-0.05x}x)