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

The answer to (\partial)/(\partial x)(xsin(2x^2y)) is sin(2x^2y)+4x^2ycos(2x^2y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xsin(2x^2y))

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

sin (2 x^{2} y) + 4 x^{2} y cos (2 x^{2} y)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (2 x^{2} y)

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

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

\frac{\partial}{\partial x} (sin (2 x^{2} y)) = cos (2 x^{2} y) \cdot 4 y x

= 1 \cdot sin (2 x^{2} y) + cos (2 x^{2} y) \cdot 4 y xx

Simplify

1 \cdot sin (2 x^{2} y) + cos (2 x^{2} y) \cdot 4 y xx : sin (2 x^{2} y) + 4 x^{2} y cos (2 x^{2} y)

= sin (2 x^{2} y) + 4 x^{2} y cos (2 x^{2} y)

\int \frac{1}{t 4 t ^{2} - 1} d t

y^{^{''}} - y = x^{2} e^{x}

\int 2 (x - 1) d x

y^{^{''}} + 2 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int_{1}^{3} (x - 1) d x

What is (\partial)/(\partial x)(xsin(2x^2y)) ?
The answer to (\partial)/(\partial x)(xsin(2x^2y)) is sin(2x^2y)+4x^2ycos(2x^2y)