What is the derivative of ye^{xy} ?

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

What is the first derivative of ye^{xy} ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

\int_{0}^{2} \frac{1}{2 - x} d x

\int (sin (x))^{- 1} d x

- x, x - x^{2}, 0, 2

\int \frac{x ^{3}}{1} + x^{4} d x

\int cos (n \cdot x) d x

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