What is (\partial)/(\partial x)(2(x-1)^2-3y-5) ?

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

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(\partial)/(\partial x)(2(x-1)^2-3y-5)

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

4 x - 4

Solution steps

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

Simplify

2 (x - 1)^{2} - 3 y - 5 : 2 x^{2} - 4 x - 3 y - 3

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (3 y) = 0

\frac{\partial}{\partial x} (3) = 0

= 4 x - 4 - 0 - 0

Simplify

= 4 x - 4

y^{^{'}} = x^{3} (1 - y)

y^{^{'}} = 0.001 y (1800 - y)

\int x \cdot e^{- x^{2}} d x

\frac{d y}{d x} = e^{x - y}, y (0) = 2

x \to 11 - lim (x - 11)

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