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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

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

arctan (x^{3})

y = \frac{x ^{3} + 3 x ^{2} - 5 x + 2}{3}

y^{^{'}} - 8 y^{3} = 0

\int \frac{1}{2 x - 1 - 4 2 x - 1} d x

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