Expert Math Class 12 Level 10

For x>0, what is d/dx(xˣ)?

x>0 के लिए d/dx(xˣ) क्या है?

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Correct Answer

A. xˣ(lnx+1)

Explanation

Step 1: Identify logarithmic differentiation. Step 2: Let y=xˣ, so ln y=xlnx; differentiating gives y'/y=lnx+1, hence y'=xˣ(lnx+1). Step 3: Exam tip: Use log differentiation when both base and power vary.

Step 1: अवधारणा logarithmic differentiation है। Step 2: y=xˣ लें, ln y=xlnx; differentiate करने पर y'/y=lnx+1, इसलिए y'=xˣ(lnx+1)। Step 3: Exam note: variable base और power हो तो log differentiation करें।

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