What is the derivative of x+y+e^{xy} ?

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

What is the first derivative of x+y+e^{xy} ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

y^{^{'}} - y = e^{3 t}

\frac{\partial}{\partial z} (\frac{x + y}{y + z})

y^{^{'}} = (x - 4) e^{- 2 y}

\frac{d}{d x} (\frac{- 2 x ^{2} + 8}{8 - x ^{2}})

\int_{0}^{\frac{π}{6}} sec (x) d x

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