What is (\partial)/(\partial x)((4x-5y)^{3/2}) ?

The answer to (\partial)/(\partial x)((4x-5y)^{3/2}) is 6(4x-5y)^{1/2}

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(\partial)/(\partial x)((4x-5y)^{3/2})

\frac{\partial}{\partial x} ((4 x - 5 y)^{\frac{3}{2}})

6 (4 x - 5 y)^{\frac{1}{2}}

Solution steps

\frac{\partial}{\partial x} ((4 x - 5 y)^{\frac{3}{2}})

Treat

y

as a constant

Apply the chain rule:

\frac{3 ( 4 x - 5 y ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - 5 y)

= \frac{3 ( 4 x - 5 y ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - 5 y)

\frac{\partial}{\partial x} (4 x - 5 y) = 4

= \frac{3 ( 4 x - 5 y ) ^{\frac{1}{2}}}{2} \cdot 4

Simplify

\frac{3 ( 4 x - 5 y ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (4 x - 5 y)^{\frac{1}{2}}

= 6 (4 x - 5 y)^{\frac{1}{2}}

\int 3 e^{- 0.2 x} d x

y^{^{'}} = \frac{( x + 3 y )}{( y - 3 x )}

sec (5 x)

f (x) = 5 x^{2} + 5 x + 7

What is (\partial)/(\partial x)((4x-5y)^{3/2}) ?
The answer to (\partial)/(\partial x)((4x-5y)^{3/2}) is 6(4x-5y)^{1/2}