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Popular Calculus >

derivative of 1000(1-e^{-0.15x})

Solution

\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

Solution

150 e^{- 0.15 x}

Solution steps

\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

Take the constant out:

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

= 1000 \frac{d}{d x} (1 - e^{- 0.15 x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 1000 (\frac{d}{d x} (1) - \frac{d}{d x} (e^{- 0.15 x}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (e^{- 0.15 x}) = - 0.15 e^{- 0.15 x}

= 1000 (0 - (- 0.15 e^{- 0.15 x}))

Simplify

= 150 e^{- 0.15 x}

Graph

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derivative of x/(x+5)

\frac{d}{d x} (\frac{x}{x + 5})

(dy)/(dx)=x(4-y)

\frac{d y}{d x} = x (4 - y)

sum from n=0 to infinity of n(3/5)^n

n = 0 \sum \infty n (\frac{3}{5})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of 1000(1-e^{-0.15x}) ?
The derivative of 1000(1-e^{-0.15x}) is 150e^{-0.15x}
What is the first derivative of 1000(1-e^{-0.15x}) ?
The first derivative of 1000(1-e^{-0.15x}) is 150e^{-0.15x}