What is the derivative of (x-ye^{xy}) ?

The derivative of (x-ye^{xy}) is (1-(dy)/(dx))e^{xy}+e^{xy}(y+x(dy)/(dx))(x-y)

What is the first derivative of (x-ye^{xy}) ?

The first derivative of (x-ye^{xy}) is (1-(dy)/(dx))e^{xy}+e^{xy}(y+x(dy)/(dx))(x-y)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x - y) = 1 - \frac{d y}{d x}

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

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

e^{y} \cdot e^{- 9 l n (y + 7)}

- (e^{x} + 1)^{5} e^{- x} \cdot e^{y}

e^{- 2.19}

e^{- 3 t} sin (2 w) t

What is the derivative of (x-ye^{xy}) ?
The derivative of (x-ye^{xy}) is (1-(dy)/(dx))e^{xy}+e^{xy}(y+x(dy)/(dx))(x-y)
What is the first derivative of (x-ye^{xy}) ?
The first derivative of (x-ye^{xy}) is (1-(dy)/(dx))e^{xy}+e^{xy}(y+x(dy)/(dx))(x-y)