What is (\partial)/(\partial x)((4x-y^2)^{3/2}) ?

The answer to (\partial)/(\partial x)((4x-y^2)^{3/2}) is 6(4x-y^2)^{1/2}

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(\partial)/(\partial x)((4x-y^2)^{3/2})

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

6 (4 x - y^{2})^{\frac{1}{2}}

Solution steps

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

Treat

y

as a constant

Apply the chain rule:

\frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - y^{2})

= \frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - y^{2})

\frac{\partial}{\partial x} (4 x - y^{2}) = 4

= \frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 4

Simplify

\frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (4 x - y^{2})^{\frac{1}{2}}

= 6 (4 x - y^{2})^{\frac{1}{2}}

n = 1 \sum \infty \frac{6}{2 ^{n}}

\frac{\partial}{\partial x} (y (1 - x))

e^{- 3 s} \cdot \frac{5}{4 s ^{2} + 16}

4 x - x^{2} (1.3)

\frac{d}{d x} (ln (e^{x} + e^{- x}))

What is (\partial)/(\partial x)((4x-y^2)^{3/2}) ?
The answer to (\partial)/(\partial x)((4x-y^2)^{3/2}) is 6(4x-y^2)^{1/2}