What is (\partial)/(\partial x)(4xsin(7x^2y)) ?

The answer to (\partial)/(\partial x)(4xsin(7x^2y)) is 4(sin(7x^2y)+14x^2ycos(7x^2y))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(4xsin(7x^2y))

\frac{\partial}{\partial x} (4 x sin (7 x^{2} y))

4 (sin (7 x^{2} y) + 14 x^{2} y cos (7 x^{2} y))

Solution steps

\frac{\partial}{\partial x} (4 x sin (7 x^{2} y))

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (x sin (7 x^{2} y))

Apply the Product Rule:

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

f = x, g = sin (7 x^{2} y)

= 4 (\frac{\partial}{\partial x} (x) sin (7 x^{2} y) + \frac{\partial}{\partial x} (sin (7 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (7 x^{2} y)) = cos (7 x^{2} y) \cdot 14 y x

= 4 (1 \cdot sin (7 x^{2} y) + cos (7 x^{2} y) \cdot 14 y xx)

Simplify

4 (1 \cdot sin (7 x^{2} y) + cos (7 x^{2} y) \cdot 14 y xx) : 4 (sin (7 x^{2} y) + 14 x^{2} y cos (7 x^{2} y))

= 4 (sin (7 x^{2} y) + 14 x^{2} y cos (7 x^{2} y))

f (x) = 3 x^{2} - 5 x

f (x) = - \frac{4}{3} x^{- \frac{5}{2}}, at x = 4

\frac{d}{d x} (x (x - 1) (x - 2))

- 4 x^{2} + 9, x + 7

What is (\partial)/(\partial x)(4xsin(7x^2y)) ?
The answer to (\partial)/(\partial x)(4xsin(7x^2y)) is 4(sin(7x^2y)+14x^2ycos(7x^2y))