What is (\partial)/(\partial x)((1+xy)^{3/2}) ?

The answer to (\partial)/(\partial x)((1+xy)^{3/2}) is (3y(1+xy)^{1/2})/2

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(\partial)/(\partial x)((1+xy)^{3/2})

\frac{\partial}{\partial x} ((1 + x y)^{\frac{3}{2}})

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

Solution steps

\frac{\partial}{\partial x} ((1 + x y)^{\frac{3}{2}})

Treat

y

as a constant

Apply the chain rule:

\frac{3 ( 1 + x y ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (1 + x y)

= \frac{3 ( 1 + x y ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (1 + x y)

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

= \frac{3 ( 1 + x y ) ^{\frac{1}{2}}}{2} y

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 y ( 1 + x y ) ^{\frac{1}{2}}}{2}

x \to \infty lim (e^{- 4 x} cos (4 x))

\int_{0}^{10} x - 5 d x

\frac{\partial}{\partial x} (- x + 345 x + 10000)

\frac{\partial}{\partial y} (y e^{\frac{x}{y}})

\frac{\partial}{\partial x} (2 y arctan (x))

What is (\partial)/(\partial x)((1+xy)^{3/2}) ?
The answer to (\partial)/(\partial x)((1+xy)^{3/2}) is (3y(1+xy)^{1/2})/2