What is (\partial)/(\partial x)(a-bx-c/y+d x/y) ?

The answer to (\partial)/(\partial x)(a-bx-c/y+d x/y) is -b+d/y

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(\partial)/(\partial x)(a-bx-c/y+d x/y)

\frac{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

- b + \frac{d}{y}

Solution steps

\frac{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

Simplify

a - b x - \frac{c}{y} + d \frac{x}{y} : a - b x + \frac{- c + x d}{y}

= \frac{\partial}{\partial x} (a - b x + \frac{- c + x d}{y})

Treat

a, b, c, d, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (a) - \frac{\partial}{\partial x} (b x) + \frac{\partial}{\partial x} (\frac{- c + x d}{y})

\frac{\partial}{\partial x} (a) = 0

\frac{\partial}{\partial x} (b x) = b

\frac{\partial}{\partial x} (\frac{- c + x d}{y}) = \frac{d}{y}

= 0 - b + \frac{d}{y}

Simplify

= - b + \frac{d}{y}

x \to 2 lim (2 x^{2} - x + 2)

(x - y) d x + (x) d y = 0

y^{^{'}} + 3 y = e^{2 x} + 1

\int 2 (2 + x^{2})^{\frac{3}{2}} x d x

(5 - 2) (58)

What is (\partial)/(\partial x)(a-bx-c/y+d x/y) ?
The answer to (\partial)/(\partial x)(a-bx-c/y+d x/y) is -b+d/y