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Question
If y = `e^(ax)`, then `x * dy/dx` = ______.
Fill in the Blanks
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Solution
If y = `e^ax`, then `x * dy/dx =` axy.
Explanation:
y = `e^(ax)`
Differentiating both sides w.r.t. x, we get
`dy/dx = e^(ax) * d/dx (ax)`
`= e^(ax) * (a)`
`= a * e^(ax)`
∴ `dy/dx` = ay
∴ `x dy/dx = axy`
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