What is (\partial)/(\partial x)(e^{2y}(3e^y-2x)) ?

The answer to (\partial)/(\partial x)(e^{2y}(3e^y-2x)) is -2e^{2y}

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(\partial)/(\partial x)(e^{2y}(3e^y-2x))

\frac{\partial}{\partial x} (e^{2 y} (3 e^{y} - 2 x))

- 2 e^{2 y}

Solution steps

\frac{\partial}{\partial x} (e^{2 y} (3 e^{y} - 2 x))

Treat

y

as a constant

Take the constant out:

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

= e^{2 y} \frac{\partial}{\partial x} (3 e^{y} - 2 x)

Apply the Sum/Difference Rule:

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

= e^{2 y} (\frac{\partial}{\partial x} (3 e^{y}) - \frac{\partial}{\partial x} (2 x))

\frac{\partial}{\partial x} (3 e^{y}) = 0

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

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

Simplify

= - 2 e^{2 y}

\frac{s + 1}{( s + 6 ) ^{2} \cdot ( s + 2 )}

\frac{d}{d x} (- e^{x - 28} + 75)

\int - x - 2 d x

f (x) = 2 x e^{x} + (x^{2} - 14) \cdot e^{x}

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

What is (\partial)/(\partial x)(e^{2y}(3e^y-2x)) ?
The answer to (\partial)/(\partial x)(e^{2y}(3e^y-2x)) is -2e^{2y}