If y = enx, then nth derivative of y is:
Look at it this way: complete solution: write formula, plug data, do arithmetic. Final value matches nny. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
#exponential
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What is e^ x x dx equal to ?
We can see that using formula we get (sin x - x cos x) + C. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get (sin x - x cos x) + C.
Ref: NCERT Mathematics Class XII — Integrals
Evaluate e^x( 1/x - 1x^2 )dx
From the definition, complete solution: write formula, plug data, do arithmetic. Final value matches e^xx + c. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
The maximum value of (1x)^x
In easy words, complete solution: write formula, plug data, do arithmetic. Final value matches e¹/e. Simple and accurate.
Ref: NCERT Mathematics Class XII — Applications of Derivatives
