Question:
1.prove thati d/dx (e^x) = e^x
2. prove that d/dx(a^x) = a^x loge a
Answer:
1. We know that, ex = 1 + x/1! + x2 /2! + x3 /3! + ..............
Now, d(ex )/dx = 0 + 1/1! + 2x /2! + 3x2 /3! + ..............
=> d(ex )/dx = 1 + x /1! + x2 /2! + ..............
=> d(ex )/dx = ex
2. Let y = ax
Take log on both side, we get
log y = x * log a
Now, (1/y)dy/dx = log a
=> dy/dx = y * log a
=> dy/dx = ax * log a
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