What is (\partial)/(\partial x)(8y-x^4sin(xy)) ?

The answer to (\partial)/(\partial x)(8y-x^4sin(xy)) is -yx^4cos(yx)-4x^3sin(yx)

Popular >

(\partial)/(\partial x)(8y-x^4sin(xy))

\frac{\partial}{\partial x} (8 y - x^{4} sin (x y))

- y x^{4} cos (y x) - 4 x^{3} sin (y x)

Solution steps

\frac{\partial}{\partial x} (8 y - x^{4} sin (x y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 y) - \frac{\partial}{\partial x} (x^{4} sin (x y))

\frac{\partial}{\partial x} (8 y) = 0

\frac{\partial}{\partial x} (x^{4} sin (x y)) = 4 x^{3} sin (x y) + cos (x y) y x^{4}

= 0 - (4 x^{3} sin (x y) + cos (x y) y x^{4})

Simplify

= - y x^{4} cos (y x) - 4 x^{3} sin (y x)

\frac{d}{d x} (- 6 x + 1)

\frac{\partial}{\partial x} (z sin (x y^{2} + 2 z))

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

\frac{\partial}{\partial x} (sin (x - y^{2}))

\int_{- 1}^{2} (x + 2 - x^{2})^{2} d x

What is (\partial)/(\partial x)(8y-x^4sin(xy)) ?
The answer to (\partial)/(\partial x)(8y-x^4sin(xy)) is -yx^4cos(yx)-4x^3sin(yx)