What is (\partial)/(\partial x)(ye^x-3x-y+5) ?

The answer to (\partial)/(\partial x)(ye^x-3x-y+5) is e^xy-3

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(\partial)/(\partial x)(ye^x-3x-y+5)

\frac{\partial}{\partial x} (y e^{x} - 3 x - y + 5)

e^{x} y - 3

Solution steps

\frac{\partial}{\partial x} (y e^{x} - 3 x - y + 5)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y e^{x}) - \frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (5)

\frac{\partial}{\partial x} (y e^{x}) = y e^{x}

\frac{\partial}{\partial x} (3 x) = 3

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

\frac{\partial}{\partial x} (5) = 0

= y e^{x} - 3 - 0 + 0

Simplify

= e^{x} y - 3

x \to 0 - lim (\frac{x ^{2} - x}{∣ x ∣})

t \to 0 lim (3)

y = \frac{3 x ^{4} + 7}{x ^{2}}

\int_{1}^{3} x 2^{x^{2}} d x

x^{2} d y + y d x = d x

What is (\partial)/(\partial x)(ye^x-3x-y+5) ?
The answer to (\partial)/(\partial x)(ye^x-3x-y+5) is e^xy-3