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

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

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

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

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

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{3 ( t ^{2} + y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 2 y : 3 y (t^{2} + y^{2})^{\frac{1}{2}}

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

f (x) = (2 x + 4)^{\frac{1}{5}}, at x = 1

y \to \infty lim (\frac{( y ^{2} - e ^{(6 y)} )}{( 4 y ^{2} + e ^{7 y} )})

h (t) = (t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3}

\frac{\partial}{\partial y} (4 x^{3} y^{3} + 1)

n = 0 \sum \infty 0. 1^{n}

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