What is (\partial)/(\partial x)(9e^y(y^2-x^2)) ?

The answer to (\partial)/(\partial x)(9e^y(y^2-x^2)) is -18e^yx

Popular >

(\partial)/(\partial x)(9e^y(y^2-x^2))

\frac{\partial}{\partial x} (9 e^{y} (y^{2} - x^{2}))

- 18 e^{y} x

Solution steps

\frac{\partial}{\partial x} (9 e^{y} (y^{2} - x^{2}))

Treat

y

as a constant

Take the constant out:

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

= 9 e^{y} \frac{\partial}{\partial x} (y^{2} - x^{2})

Apply the Sum/Difference Rule:

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

= 9 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

= 9 e^{y} (0 - 2 x)

Simplify

= - 18 e^{y} x

\int t ln (t + 4) d t

\frac{d}{d x} (\frac{36 x}{x ^{2} + 36})

f (x) = (4 + 5 x)^{2}, (- 3, 121)

f (x) = 2 x, (18, 6)

What is (\partial)/(\partial x)(9e^y(y^2-x^2)) ?
The answer to (\partial)/(\partial x)(9e^y(y^2-x^2)) is -18e^yx