What is (\partial)/(\partial x)(x*e^{xy+1}) ?

The answer to (\partial)/(\partial x)(x*e^{xy+1}) is e^{xy+1}+e^{xy+1}xy

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(\partial)/(\partial x)(x*e^{xy+1})

\frac{\partial}{\partial x} (x \cdot e^{x y + 1})

e^{x y + 1} + e^{x y + 1} x y

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{x y + 1} + e^{x y + 1} y x

Simplify

= e^{x y + 1} + e^{x y + 1} x y

x \to \infty lim (\frac{cos ( 21 x )}{21 x})

\frac{d}{d x} (\frac{2}{5} x)

\frac{d y}{d x} = 3 x^{4} - 6 x^{3} + 3 x - 8

f (x) = 5 x^{3} - 5 x^{2} + 2, (1, 2)

x \to - 1 - lim (3 x + 3 - 5)

What is (\partial)/(\partial x)(x*e^{xy+1}) ?
The answer to (\partial)/(\partial x)(x*e^{xy+1}) is e^{xy+1}+e^{xy+1}xy