Question

Find y"' if y = e^(-3x)​

Answer 1

Answer:

$\bull{y' = - \frac{3}{e {}^{3x} }}$

Explanation:

$\longrightarrow \: y = e {}^{ - 3x}$

[ Take the derivative ]

$\longrightarrow \: y' = \frac{d}{dx} (e {}^{ -3 x} )$

[ Using defferentuition rule ]

$\longrightarrow \: y' = \frac{d}{dg} (e {}^{g} ) \times \frac{d}{dx} ( - 3x)$

[ Differentiate ]

$\longrightarrow \: y' = e {}^{g} \times - 3$

[ Substitute back ]

$\longrightarrow \: y' = e {}^{ - 3x} \times - 3$

[ Simplify ]

$\longrightarrow \red{y' = - \frac{3}{e {}^{3x} } }$

Answer 2

Explanation:

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