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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{y^{2} - x^{2}} (- 2 x)

Simplify

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

\int \frac{1}{8} cos (2 x) d x

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\frac{d y}{d x} = \frac{3 x + x y ^{2}}{2 y + x ^{2} y}

\frac{d}{d x} (x (ln (5 x))^{2})

\frac{d y}{d t} = (k (y - 60))

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