What is (\partial)/(\partial x)(4xcos(5xy)) ?

The answer to (\partial)/(\partial x)(4xcos(5xy)) is 4(cos(5xy)-5xysin(5xy))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(4xcos(5xy))

\frac{\partial}{\partial x} (4 x cos (5 x y))

4 (cos (5 x y) - 5 x y sin (5 x y))

Solution steps

\frac{\partial}{\partial x} (4 x cos (5 x y))

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (x cos (5 x y))

Apply the Product Rule:

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

f = x, g = cos (5 x y)

= 4 (\frac{\partial}{\partial x} (x) cos (5 x y) + \frac{\partial}{\partial x} (cos (5 x y)) x)

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

\frac{\partial}{\partial x} (cos (5 x y)) = - sin (5 x y) \cdot 5 y

= 4 (1 \cdot cos (5 x y) + (- sin (5 x y) \cdot 5 y) x)

Simplify

= 4 (cos (5 x y) - 5 x y sin (5 x y))

t^{3} \cdot e^{- 3 t}

\int 5 e^{- 3 x} d x

\frac{9 - x e ^{x}}{x + e ^{x}}

n = 1 \sum \infty ln (cos (n))

a cos (t) + t^{2} sin (t)

What is (\partial)/(\partial x)(4xcos(5xy)) ?
The answer to (\partial)/(\partial x)(4xcos(5xy)) is 4(cos(5xy)-5xysin(5xy))