Question

x^(x^2 - 3)+(x-3)^x^2 , forx>3

Answer 1

question is ------> Differentiate w.r.t. x the function x^(x² -3) + (x - 3)^{x²} , for x > 3

solution :- Let y = x^(x² -3) + (x - 3)^x²
y = e^{(x² -3)lnx } + e^{x²ln(x -3)}
differentiate with respect to x,
dy/dx = d[e^{(x²-3)lnx}]/dx + d[e^{x²ln(x -3)}]/dx

= e^{(x²-3)lnx} d[(x²-3)lnx]/dx + e^{x²ln(x-3)}.d[x²ln(x-3)]/dx

= e^{(x²-3)lnx} × [(x²-3). d(lnx)/dx + lnx. d(x²-3)/dx] + e^{x²ln(x-3)}[ln(x-3).d(x²)/dx + x².d{ln(x-3)}/dx]

= e^{(x²-3)lnx} [(x²-3)/x + 2xlnx] + e^{x²ln(x-3)} [2xln(x-3) + x²/(x -3)]

= x^(x² -3) [(x²-3)/x + 2xlnx] + (x-3)^x²[2xln(x-3) + x²/(x -3)]

Answer 2

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