What is the derivative of e^{x^2-y^2} ?

The derivative of e^{x^2-y^2} is e^{x^2-y^2}*2x

What is the first derivative of e^{x^2-y^2} ?

The first derivative of e^{x^2-y^2} is e^{x^2-y^2}*2x

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derivative

e^{x^{2} - y^{2}} \cdot 2 x

Solution steps

\frac{d}{d x} (e^{x^{2} - y^{2}})

Treat

y

as a constant

Apply the chain rule:

e^{x^{2} - y^{2}} \frac{d}{d x} (x^{2} - y^{2})

= e^{x^{2} - y^{2}} \frac{d}{d x} (x^{2} - y^{2})

\frac{d}{d x} (x^{2} - y^{2}) = 2 x

= e^{x^{2} - y^{2}} \cdot 2 x

What is the derivative of e^{x^2-y^2} ?
The derivative of e^{x^2-y^2} is e^{x^2-y^2}*2x
What is the first derivative of e^{x^2-y^2} ?
The first derivative of e^{x^2-y^2} is e^{x^2-y^2}*2x