What is (\partial)/(\partial x)(e^{(x^2-y^2)}) ?

The answer to (\partial)/(\partial x)(e^{(x^2-y^2)}) is e^{x^2-y^2}*2x

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(\partial)/(\partial x)(e^{(x^2-y^2)})

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

(36 - x^{2}) \frac{d y}{d x} = 1

\int_{0}^{\frac{π}{3}} (tan (x))^{2} d x

\int 9 ln (x^{2} - 1) d x

y^{^{'}} + \frac{y}{x} = \frac{y ^{2}}{x}

\frac{d}{d x} (x^{4} - 5 x^{2} + 4)

What is (\partial)/(\partial x)(e^{(x^2-y^2)}) ?
The answer to (\partial)/(\partial x)(e^{(x^2-y^2)}) is e^{x^2-y^2}*2x