Question

Question #88d66

Answer 1

`y=x^{x^2}`

By taking the natural log,

`Rightarrow lny=lnx^{x^2}`

by the log property `ln x^r=rln x`,

`Rightarrow lny=x^2 lnx`

by differentiating implicitly,

`Rightarrow {y'}/y=2xcdotlnx+x^2cdot 1/x=(2lnx+1)x`

by multiplying by `y=x^{x^2}`,

`Rightarrow y'=(2lnx+1)x^{x^2+1}`.

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I hope that this was helpful.