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

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

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

x \to 2 lim (3 x - 6)

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

f (x) = sin^{3} (2 x)

y = 8 x^{3} - 5 x^{2} - \frac{x}{12}

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