What is the derivative of e^{xe^y} ?

The derivative of e^{xe^y} is e^{xe^y}(e^y+e^yx(dy)/(dx))

What is the first derivative of e^{xe^y} ?

The first derivative of e^{xe^y} is e^{xe^y}(e^y+e^yx(dy)/(dx))

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\frac{d}{d x} (e^{x e^{y}})

e^{x e^{y}} (e^{y} + e^{y} x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (e^{x e^{y}})

Apply the chain rule:

e^{x e^{y}} \frac{d}{d x} (x e^{y})

= e^{x e^{y}} \frac{d}{d x} (x e^{y})

\frac{d}{d x} (x e^{y}) = e^{y} + e^{y} x \frac{d y}{d x}

= e^{x e^{y}} (e^{y} + e^{y} x \frac{d y}{d x})

What is the derivative of e^{xe^y} ?
The derivative of e^{xe^y} is e^{xe^y}(e^y+e^yx(dy)/(dx))
What is the first derivative of e^{xe^y} ?
The first derivative of e^{xe^y} is e^{xe^y}(e^y+e^yx(dy)/(dx))