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

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

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

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

- 2 x

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (1) = 0

= 0 - 2 x - 0

Simplify

= - 2 x

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

f (x) = (x + 1)^{x + 1}

y = sin (9 x) + cos (7 x)

\frac{d}{d x} (2 - 5 x^{2})

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