en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y))

Solution

\frac{\partial}{\partial x} (e^{- 3 π t} cos (4 x) sin (6 y))

Solution

- 4 e^{- 3 π t} sin (4 x) sin (6 y)

Solution steps

\frac{\partial}{\partial x} (e^{- 3 π t} cos (4 x) sin (6 y))

Treat

t, y

as constants

Take the constant out:

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

= e^{- 3 π t} sin (6 y) \frac{\partial}{\partial x} (cos (4 x))

Apply the chain rule:

- sin (4 x) \frac{\partial}{\partial x} (4 x)

= - sin (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= e^{- 3 π t} sin (6 y) (- sin (4 x) \cdot 4)

Simplify

= - 4 e^{- 3 π t} sin (4 x) sin (6 y)

Popular Examples

derivative of y=in(x)derivative of

y = in (x)

integral from 0 to 9 of 1/((x-1)^{2/3)}

\int_{0}^{9} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

(\partial)/(\partial x)(e^{-2y}sin(3x))

\frac{\partial}{\partial x} (e^{- 2 y} sin (3 x))

integral of tec(2t)

\int t ec (2 t) d t

derivative of (x+1*(x^2-1))

\frac{d}{d x} ((x + 1) \cdot (x^{2} - 1))

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y)) ?
The answer to (\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y)) is -4e^{-3pit}sin(4x)sin(6y)