What is the derivative of xe^{xy}+2xy+1/x ?

The derivative of xe^{xy}+2xy+1/x is e^{xy}+e^{xy}x(y+x(dy)/(dx))+2(y+x(dy)/(dx))-1/(x^2)

What is the first derivative of xe^{xy}+2xy+1/x ?

The first derivative of xe^{xy}+2xy+1/x is e^{xy}+e^{xy}x(y+x(dy)/(dx))+2(y+x(dy)/(dx))-1/(x^2)

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\frac{d}{d x} (x e^{x y} + 2 x y + \frac{1}{x})

e^{x y} + e^{x y} x (y + x \frac{d y}{d x}) + 2 (y + x \frac{d y}{d x}) - \frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (x e^{x y} + 2 x y + \frac{1}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x e^{x y}) + \frac{d}{d x} (2 x y) + \frac{d}{d x} (\frac{1}{x})

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

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

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= e^{x y} + e^{x y} x (y + x \frac{d y}{d x}) + 2 (y + x \frac{d y}{d x}) - \frac{1}{x ^{2}}

y^{^{'}} - e^{y} - 2 x e^{y} = 0

y = sin (tan (7 x))

\frac{\partial}{\partial x} (4 x (3 + y)^{- 1})

\int 56 cos (8 x - 5) d x

\int_{0}^{\infty} (x e^{- x}) d x

What is the derivative of xe^{xy}+2xy+1/x ?
The derivative of xe^{xy}+2xy+1/x is e^{xy}+e^{xy}x(y+x(dy)/(dx))+2(y+x(dy)/(dx))-1/(x^2)
What is the first derivative of xe^{xy}+2xy+1/x ?
The first derivative of xe^{xy}+2xy+1/x is e^{xy}+e^{xy}x(y+x(dy)/(dx))+2(y+x(dy)/(dx))-1/(x^2)