What is (\partial)/(\partial x)(xzsqrt(x+y)) ?

The answer to (\partial)/(\partial x)(xzsqrt(x+y)) is (z(3x+2y))/(2sqrt(x+y))

(\partial)/(\partial x)(xzsqrt(x+y))

\frac{\partial}{\partial x} (x z x + y)

\frac{z ( 3 x + 2 y )}{2 x + y}

Solution steps

\frac{\partial}{\partial x} (x z x + y)

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x + y

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x + y) = \frac{1}{2 x + y}

= z (1 \cdot x + y + \frac{1}{2 x + y} x)

Simplify

z (1 \cdot x + y + \frac{1}{2 x + y} x) : \frac{z ( 3 x + 2 y )}{2 x + y}

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

\int - 5 x^{4} e^{x^{5}} d x

d er i v a t i v e f (x) = \frac{x}{32} (x + 3 x)

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

\frac{d}{d x} ((x^{3} + 6 x)^{4})

in v erse l a pl a ce \frac{2 e ^{- 2 s}}{3 s ^{2} + 12}

What is (\partial)/(\partial x)(xzsqrt(x+y)) ?
The answer to (\partial)/(\partial x)(xzsqrt(x+y)) is (z(3x+2y))/(2sqrt(x+y))