What is (\partial)/(\partial x)(x^3e^ysin(x-y)) ?

The answer to (\partial)/(\partial x)(x^3e^ysin(x-y)) is e^y(3x^2sin(x-y)+cos(x-y)x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x^3e^ysin(x-y))

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

e^{y} (3 x^{2} sin (x - y) + cos (x - y) x^{3})

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{3}, g = sin (x - y)

= e^{y} (\frac{\partial}{\partial x} (x^{3}) sin (x - y) + \frac{\partial}{\partial x} (sin (x - y)) x^{3})

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

\frac{\partial}{\partial x} (sin (x - y)) = cos (x - y)

= e^{y} (3 x^{2} sin (x - y) + cos (x - y) x^{3})

7 sin (5 x)

\int \frac{1}{x ^{3} + 2} d x

f (x) = x^{2} - 3, (3, 6)

\frac{d y}{d x} = 3 x e^{y}, y (0) = 0

\int_{1}^{7} \frac{2 ln ( x )}{x} d x

What is (\partial)/(\partial x)(x^3e^ysin(x-y)) ?
The answer to (\partial)/(\partial x)(x^3e^ysin(x-y)) is e^y(3x^2sin(x-y)+cos(x-y)x^3)