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

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

Popular >

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

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

3 x^{2} y^{2} + 2 x^{4}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 x^{2} y^{2} + 2 x^{4}

\frac{d}{d x} (7 - 10 x)

\int \frac{sin ( x )}{5 + cos ^{2} ( x )} d x

\frac{d}{d x} (1 - ∣ 1 - x ∣)

\int \frac{x ^{4}}{x} d x

(x^{2} + 2)^{2} y = \frac{5 x ( y ^{2} + 1 ) ^{2}}{( x ^{2} + 2 ) y ^{^{'}}} - (x^{4} + 4 x^{2} + 4) y

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