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

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

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

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

- 2 e^{y} x

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y^{2}) = 0

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

= e^{y} (0 - 2 x)

Simplify

= - 2 e^{y} x

(tan (x))^{^{'}}

y = - 2 x^{3}, (- 2, 16)

x \to 0 lim ((1 - 2 x)^{\frac{4}{x}})

\int \frac{2 y}{3} d y

\int \frac{( y - 4 )}{y ^{2} - 8 y + 10} d y

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