For y=x^(7x), what is dy/dx?
y=x^(7x) के लिए dy/dx क्या है?
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Correct Answer
C. 7x^(7x)(ln x + 1)
ExplanationStep 1: use logarithmic differentiation: ln y=7x ln x. Step 2: differentiating gives y'/y=7(ln x+1), so y'=7x^(7x)(ln x+1). Step 3: tip: when base and power both vary, take log first.
Step 1: logarithmic differentiation use करें: ln y=7x ln x। Step 2: differentiate करने पर y'/y=7(ln x+1), इसलिए y'=7x^(7x)(ln x+1)। Step 3: tip: variable base और variable power हो तो log लें।