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Question
Differentiate the following w.r.t. x:
`e^x + e^(x^2) + "..." + e^(x^5)`
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Solution
`e^x + e^(x^2) + "..." + e^(x^5)`
Differentiating both sides with respect to x,
`dy/dx = d/dx (e^x + e^(x^2) + "..." + e^(x^5))`
= `d/dx (e^x) + d/dx (e^(x^2)) + d/dx (e^(x^3)) + d/dx (e^(x^4)) + d/dx (e^(x^5))`
= `e^x + e^(x^2) d/dx (x^2) + e^(x^3) d/dx (x^3) + e^(x^4) d/dx (x^4) + e^(x^5) d/dx (x^5)`
= `e^x + e^(x^2). 2 x + e^(x^3). 3x^2 + e^(x^4) .4x^3 + e^(x^5). 5x^4`
= `e^x + 2xe^(x^2) + 3x^2 e^(x^3) + 4x^3 e^(x^4) + 5x^4 e^(x^5)`
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