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

The answer to (\partial)/(\partial x)(2x^2e^y) is 4e^yx

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

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

4 e^{y} x

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 e^{y} \cdot 2 x^{2 - 1}

Simplify

= 4 e^{y} x

\frac{d}{d x} ((x^{2} + 4)^{- 2})

\frac{d y}{d t} = b (1 - y) y

x \to - 9 + lim (3 x^{2} - 4 x - 7)

\int sin (θ) (cot (θ) + csc (θ)) d θ

\frac{\partial}{\partial x} (6 x + 6 y^{2})

What is (\partial)/(\partial x)(2x^2e^y) ?
The answer to (\partial)/(\partial x)(2x^2e^y) is 4e^yx