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

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

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

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

4 x + 3 z

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

\frac{\partial}{\partial y} (3 yz) = 3 z

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

= 0 + 3 z + 4 x

Simplify

= 4 x + 3 z

\frac{d}{d x} (\frac{3}{x ^{2}} + \frac{5}{x ^{4}})

f (x) = x^{2} \cdot ln (x)

\int x e^{- 5 x} d x

\int (tan (θ) + cot (θ))^{2} d θ

\int \frac{6}{x} + 6 x d x

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