What is (\partial)/(\partial x)(e^{3x^2y}(1+x-2y)) ?

The answer to (\partial)/(\partial x)(e^{3x^2y}(1+x-2y)) is 6e^{3x^2y}xy(1+x-2y)+e^{3x^2y}

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(\partial)/(\partial x)(e^{3x^2y}(1+x-2y))

\frac{\partial}{\partial x} (e^{3 x^{2} y} (1 + x - 2 y))

6 e^{3 x^{2} y} x y (1 + x - 2 y) + e^{3 x^{2} y}

Solution steps

\frac{\partial}{\partial x} (e^{3 x^{2} y} (1 + x - 2 y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{3 x^{2} y}, g = 1 + x - 2 y

= \frac{\partial}{\partial x} (e^{3 x^{2} y}) (1 + x - 2 y) + \frac{\partial}{\partial x} (1 + x - 2 y) e^{3 x^{2} y}

\frac{\partial}{\partial x} (e^{3 x^{2} y}) = e^{3 x^{2} y} \cdot 6 y x

\frac{\partial}{\partial x} (1 + x - 2 y) = 1

= e^{3 x^{2} y} \cdot 6 y x (1 + x - 2 y) + 1 \cdot e^{3 x^{2} y}

Simplify

= 6 e^{3 x^{2} y} x y (1 + x - 2 y) + e^{3 x^{2} y}

\frac{d}{d x} (9 - 4 x)

\int π (x + 1)^{2} d x

(x, y) \to (0, 9) lim (x^{3} y)

\frac{\partial}{\partial x} (e^{x \cdot c o s (y)})

- 5 (t - 2) e^{t - 2}

What is (\partial)/(\partial x)(e^{3x^2y}(1+x-2y)) ?
The answer to (\partial)/(\partial x)(e^{3x^2y}(1+x-2y)) is 6e^{3x^2y}xy(1+x-2y)+e^{3x^2y}