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Popular >

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

Solution

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

Solution

2 x y^{2} + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

= 2 x y^{2} + y

Popular Examples

derivative of 6x^{3/2}+1

\frac{d}{d x} (6 x^{\frac{3}{2}} + 1)

integral of cos^2(3x)

\int cos^{2} (3 x) d x

f(x)=arcsin(2x+1)

f (x) = arcsin (2 x + 1)

derivative of sqrt(x^2-2x+2)(x+1)

\frac{d}{d x} (x^{2} - 2 x + 2 (x + 1))

derivative of (sqrt(x)-1/(x-1))

\frac{d}{d x} (\frac{x - 1}{x - 1})

Frequently Asked Questions (FAQ)

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