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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

1 \cdot e^{x^{2} - y} + e^{x^{2} - y} \cdot 2 xx : e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}

= e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}

x \to 0 lim (\frac{9 e ^{x} - 9}{x})

f (x) = 4 sec (4 x)

\int (6 x^{5} + 7) x^{6} + 7 x d x

lo g_{e} (sec (\frac{1}{5 x}))

\frac{5}{s ^{2}}

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