What is (\partial)/(\partial x)(2ye^{4x^2-6y}) ?

The answer to (\partial)/(\partial x)(2ye^{4x^2-6y}) is 16e^{4x^2-6y}yx

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(\partial)/(\partial x)(2ye^{4x^2-6y})

\frac{\partial}{\partial x} (2 y e^{4 x^{2} - 6 y})

16 e^{4 x^{2} - 6 y} y x

Solution steps

\frac{\partial}{\partial x} (2 y e^{4 x^{2} - 6 y})

Treat

y

as a constant

Take the constant out:

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

= 2 y \frac{\partial}{\partial x} (e^{4 x^{2} - 6 y})

Apply the chain rule:

e^{4 x^{2} - 6 y} \frac{\partial}{\partial x} (4 x^{2} - 6 y)

= e^{4 x^{2} - 6 y} \frac{\partial}{\partial x} (4 x^{2} - 6 y)

\frac{\partial}{\partial x} (4 x^{2} - 6 y) = 8 x

= 2 y e^{4 x^{2} - 6 y} \cdot 8 x

Simplify

= 16 e^{4 x^{2} - 6 y} y x

f (x) = - x

x \to \infty lim (- 3, x)

\frac{d}{d x} ((x + 1)^{2} e^{x})

x \to \frac{9 π}{2} lim (sec (x))

What is (\partial)/(\partial x)(2ye^{4x^2-6y}) ?
The answer to (\partial)/(\partial x)(2ye^{4x^2-6y}) is 16e^{4x^2-6y}yx