What is the derivative of xe^{yx} ?

The derivative of xe^{yx} is e^{xy}+e^{xy}x(x(dy)/(dx)+y)

What is the first derivative of xe^{yx} ?

The first derivative of xe^{yx} is e^{xy}+e^{xy}x(x(dy)/(dx)+y)

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\frac{d}{d x} (x e^{y x})

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

Solution steps

\frac{d}{d x} (x e^{y x})

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\frac{d}{d x} (e^{- x} cos (3 x))

\int_{1}^{3} t ln (t) d t

(\frac{1}{5}) (x y^{2} + 4 y)^{2}

\int x \cdot cos (x) d x

What is the derivative of xe^{yx} ?
The derivative of xe^{yx} is e^{xy}+e^{xy}x(x(dy)/(dx)+y)
What is the first derivative of xe^{yx} ?
The first derivative of xe^{yx} is e^{xy}+e^{xy}x(x(dy)/(dx)+y)