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

The answer to (\partial)/(\partial y)(2x^3+x^2y+3xy^2) is x^2+6xy

Popular >

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

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

x^{2} + 6 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (2 x^{3}) = 0

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

\frac{\partial}{\partial y} (3 x y^{2}) = 6 x y

= 0 + x^{2} + 6 x y

Simplify

= x^{2} + 6 x y

y = x^{2} + 3

\int \frac{7 x}{e ^{x^{2}}} d x

\int \frac{1}{x ^{3}} + \frac{6}{x ^{7}} d x

n = 0 \sum \infty \frac{1}{( 2 + 2 n ) ^{3}}

\int_{- 1}^{3} 2 x^{2} + 8 d x

What is (\partial)/(\partial y)(2x^3+x^2y+3xy^2) ?
The answer to (\partial)/(\partial y)(2x^3+x^2y+3xy^2) is x^2+6xy