What is (\partial)/(\partial x)(sqrt(3x+2y-3)) ?

The answer to (\partial)/(\partial x)(sqrt(3x+2y-3)) is 3/(2sqrt(3x+2y-3))

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(\partial)/(\partial x)(sqrt(3x+2y-3))

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

\frac{3}{2 3 x + 2 y - 3}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 3 x + 2 y - 3} \cdot 3

Simplify

\frac{1}{2 3 x + 2 y - 3} \cdot 3 : \frac{3}{2 3 x + 2 y - 3}

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

y = x^{2}, y = 3 - x, (0, 1.3)

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 1)

\int - \frac{8}{x ^{2}} d x

y^{^{'}} = 18.2 - 0.7 y

y^{^{'}} = 1 - \frac{2 y}{100 + 2 x}, y (0) = 20

What is (\partial)/(\partial x)(sqrt(3x+2y-3)) ?
The answer to (\partial)/(\partial x)(sqrt(3x+2y-3)) is 3/(2sqrt(3x+2y-3))