Question
Download Solution PDFFind the derivative of 2-3x with respect to x
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Formula:
log mn = n log m
\(\rm \frac{d(uv)}{dx} = v\frac{du}{dx}+u\frac{dv}{dx}\)
\(\rm \frac{d\log x}{dx} = \frac{1}{x}\)
Calculation:
Let y = 2-3x
Taking log both sides, we get
⇒ log y = log 2-3x
⇒ log y = -3x log 2 (∵ log mn = n log m)
⇒ log y = (-3log 2) x
differentiating with respect to x
⇒ \(\rm \frac 1 y \frac{dy}{dx} \) = (-3log 2) × 1
⇒ \(\rm \frac{dy}{dx} \) = (-3log 2)y
∴ \(\rm \frac{dy}{dx} \) = (-3log 2)2-3x
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