What is the derivative of 2y+xe^y ?

The derivative of 2y+xe^y is 2(dy)/(dx)+e^y+e^yx(dy)/(dx)

What is the first derivative of 2y+xe^y ?

The first derivative of 2y+xe^y is 2(dy)/(dx)+e^y+e^yx(dy)/(dx)

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\frac{d}{d x} (2 y + x e^{y})

2 \frac{d y}{d x} + e^{y} + e^{y} x \frac{d y}{d x}

Solution steps

\frac{d}{d x} (2 y + x e^{y})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 y) = 2 \frac{d y}{d x}

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

= 2 \frac{d y}{d x} + e^{y} + e^{y} x \frac{d y}{d x}

\frac{d y}{d t} - \frac{2}{t} y = t^{5}

\int (\frac{1}{x} - \frac{5}{x ^{2} + 1}) d x

\frac{s + 2}{s ( s + 2 ) + 1}

\frac{d}{d x} (\frac{3 x + 1}{2 x - 1})

\frac{1}{s ( s + 4 )}

What is the derivative of 2y+xe^y ?
The derivative of 2y+xe^y is 2(dy)/(dx)+e^y+e^yx(dy)/(dx)
What is the first derivative of 2y+xe^y ?
The first derivative of 2y+xe^y is 2(dy)/(dx)+e^y+e^yx(dy)/(dx)