What is (\partial)/(\partial x)((x^2+y)e^{3x+4y}) ?

The answer to (\partial)/(\partial x)((x^2+y)e^{3x+4y}) is 2xe^{3x+4y}+e^{3x+4y}*3(x^2+y)

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(\partial)/(\partial x)((x^2+y)e^{3x+4y})

\frac{\partial}{\partial x} ((x^{2} + y) e^{3 x + 4 y})

2 x e^{3 x + 4 y} + e^{3 x + 4 y} \cdot 3 (x^{2} + y)

Solution steps

\frac{\partial}{\partial x} ((x^{2} + y) e^{3 x + 4 y})

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{2} + y, g = e^{3 x + 4 y}

= \frac{\partial}{\partial x} (x^{2} + y) e^{3 x + 4 y} + \frac{\partial}{\partial x} (e^{3 x + 4 y}) (x^{2} + y)

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

\frac{\partial}{\partial x} (e^{3 x + 4 y}) = e^{3 x + 4 y} \cdot 3

= 2 x e^{3 x + 4 y} + e^{3 x + 4 y} \cdot 3 (x^{2} + y)

\frac{d y}{d x} = 3 y + y^{4}

\int x 1 + x^{2} d x

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

x \to 2 lim (4 x - 3)

\frac{d}{d x} (sin (\frac{1}{x}))

What is (\partial)/(\partial x)((x^2+y)e^{3x+4y}) ?
The answer to (\partial)/(\partial x)((x^2+y)e^{3x+4y}) is 2xe^{3x+4y}+e^{3x+4y}*3(x^2+y)