What is (\partial)/(\partial x)(21y^3cos(7y^2x)) ?

The answer to (\partial)/(\partial x)(21y^3cos(7y^2x)) is -147y^5sin(7y^2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(21y^3cos(7y^2x))

\frac{\partial}{\partial x} (21 y^{3} cos (7 y^{2} x))

- 147 y^{5} sin (7 y^{2} x)

Solution steps

\frac{\partial}{\partial x} (21 y^{3} cos (7 y^{2} x))

Treat

y

as a constant

Take the constant out:

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

= 21 y^{3} \frac{\partial}{\partial x} (cos (7 y^{2} x))

Apply the chain rule:

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

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

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

= 21 y^{3} (- sin (7 y^{2} x) \cdot 7 y^{2})

Simplify

21 y^{3} (- sin (7 y^{2} x) \cdot 7 y^{2}) : - 147 y^{5} sin (7 y^{2} x)

= - 147 y^{5} sin (7 y^{2} x)

\frac{d}{d x} (sin^{2} (π x))

\frac{d y}{d x} = \frac{2 sec ( y )}{( x - 2 ) ^{2}}

\frac{\partial}{\partial y} (x e^{2 y + 3 z})

\int e^{- ia x} d x

What is (\partial)/(\partial x)(21y^3cos(7y^2x)) ?
The answer to (\partial)/(\partial x)(21y^3cos(7y^2x)) is -147y^5sin(7y^2x)