What is (\partial)/(\partial x)(x^3+y^3-27x-12y) ?

The answer to (\partial)/(\partial x)(x^3+y^3-27x-12y) is 3x^2-27

Popular >

(\partial)/(\partial x)(x^3+y^3-27x-12y)

\frac{\partial}{\partial x} (x^{3} + y^{3} - 27 x - 12 y)

3 x^{2} - 27

Solution steps

\frac{\partial}{\partial x} (x^{3} + y^{3} - 27 x - 12 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (27 x) - \frac{\partial}{\partial x} (12 y)

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

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

\frac{\partial}{\partial x} (27 x) = 27

\frac{\partial}{\partial x} (12 y) = 0

= 3 x^{2} + 0 - 27 - 0

Simplify

= 3 x^{2} - 27

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

\int t^{3} ln (t^{2}) d t

(- 2 cos (2 x) - sin (3 x) - 3)^{2}

y^{^{''}} + y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{v ^{2}}{v ^{2} - 1} d v

What is (\partial)/(\partial x)(x^3+y^3-27x-12y) ?
The answer to (\partial)/(\partial x)(x^3+y^3-27x-12y) is 3x^2-27