What is (\partial)/(\partial x)(sin^3(x^2y)) ?

The answer to (\partial)/(\partial x)(sin^3(x^2y)) is 6xysin^2(x^2y)cos(x^2y)

Popular >

(\partial)/(\partial x)(sin^3(x^2y))

\frac{\partial}{\partial x} (sin^{3} (x^{2} y))

6 x y sin^{2} (x^{2} y) cos (x^{2} y)

Solution steps

\frac{\partial}{\partial x} (sin^{3} (x^{2} y))

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (sin (x^{2} y)) = cos (x^{2} y) \cdot 2 y x

= 3 (sin (x^{2} y))^{2} cos (x^{2} y) \cdot 2 y x

Simplify

= 6 x y sin^{2} (x^{2} y) cos (x^{2} y)

\frac{d y}{d x} + 3 y x^{3} = 0

\int t^{2} sin (n t) d t

x \to e + lim ((ln (x))^{\frac{1}{x - e}})

y^{^{''}} + 9 y = e^{t} (cos (3 t) + sin (3 t))

x \to 9 lim (7 x + ∣ x - 9 ∣)

What is (\partial)/(\partial x)(sin^3(x^2y)) ?
The answer to (\partial)/(\partial x)(sin^3(x^2y)) is 6xysin^2(x^2y)cos(x^2y)