What is (\partial)/(\partial x)(2x-3y+4xy) ?

The answer to (\partial)/(\partial x)(2x-3y+4xy) is 4y+2

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(\partial)/(\partial x)(2x-3y+4xy)

\frac{\partial}{\partial x} (2 x - 3 y + 4 x y)

4 y + 2

Solution steps

\frac{\partial}{\partial x} (2 x - 3 y + 4 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x) - \frac{\partial}{\partial x} (3 y) + \frac{\partial}{\partial x} (4 x y)

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (3 y) = 0

\frac{\partial}{\partial x} (4 x y) = 4 y

= 2 - 0 + 4 y

Simplify

= 4 y + 2

\int \frac{2}{1 + 3 x} d x

r \frac{d r}{d θ} = sin^{2} (θ)

\frac{\partial ^{2}}{\partial y ^{2}} (ln (x^{2} + y^{2}))

(ln (2 x))^{^{'}}

\int_{b}^{1} 8 ln (x) d x

What is (\partial)/(\partial x)(2x-3y+4xy) ?
The answer to (\partial)/(\partial x)(2x-3y+4xy) is 4y+2