What is (\partial)/(\partial x)(8x^3y-7y^2+2x) ?

The answer to (\partial)/(\partial x)(8x^3y-7y^2+2x) is 24x^2y+2

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(\partial)/(\partial x)(8x^3y-7y^2+2x)

\frac{\partial}{\partial x} (8 x^{3} y - 7 y^{2} + 2 x)

24 x^{2} y + 2

Solution steps

\frac{\partial}{\partial x} (8 x^{3} y - 7 y^{2} + 2 x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x^{3} y) - \frac{\partial}{\partial x} (7 y^{2}) + \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (8 x^{3} y) = 24 y x^{2}

\frac{\partial}{\partial x} (7 y^{2}) = 0

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

= 24 y x^{2} - 0 + 2

Simplify

= 24 x^{2} y + 2

f (x) = 2 cos (x), at x = \frac{π}{3}

\frac{d}{d x} (x^{2} + 15)

x \to - 2 lim (- 7)

\int (4 x + 3) (2 x^{2} + 3 x) d x

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

What is (\partial)/(\partial x)(8x^3y-7y^2+2x) ?
The answer to (\partial)/(\partial x)(8x^3y-7y^2+2x) is 24x^2y+2