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Popular >

derivative of y=-25+5x+10e^{-x/5+1}

Solution

derivative of

y = - 25 + 5 x + 10 e^{- \frac{x}{5} + 1}

Solution

- 2 e^{- \frac{x}{5} + 1} + 5

Solution steps

\frac{d}{d x} (- 25 + 5 x + 10 e^{- \frac{x}{5} + 1})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (25) + \frac{d}{d x} (5 x) + \frac{d}{d x} (10 e^{- \frac{x}{5} + 1})

\frac{d}{d x} (25) = 0

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

\frac{d}{d x} (10 e^{- \frac{x}{5} + 1}) = - 2 e^{- \frac{x}{5} + 1}

= - 0 + 5 - 2 e^{- \frac{x}{5} + 1}

Simplify

= - 2 e^{- \frac{x}{5} + 1} + 5

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y^{^{'}} - 7.5 y = - 12 y^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of y=-25+5x+10e^{-x/5+1} ?
The derivative of y=-25+5x+10e^{-x/5+1} is -2e^{-x/5+1}+5
What is the first derivative of y=-25+5x+10e^{-x/5+1} ?
The first derivative of y=-25+5x+10e^{-x/5+1} is -2e^{-x/5+1}+5