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Popular >

(\partial)/(\partial x)(e^{-2t}cos(2x))

Solution

\frac{\partial}{\partial x} (e^{- 2 t} cos (2 x))

Solution

- 2 e^{- 2 t} sin (2 x)

Solution steps

\frac{\partial}{\partial x} (e^{- 2 t} cos (2 x))

Treat

t

as a constant

Take the constant out:

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

= e^{- 2 t} \frac{\partial}{\partial x} (cos (2 x))

Apply the chain rule:

- sin (2 x) \frac{\partial}{\partial x} (2 x)

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

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

= e^{- 2 t} (- sin (2 x) \cdot 2)

Simplify

= - 2 e^{- 2 t} sin (2 x)

Popular Examples

(\partial)/(\partial x)(sec(x)tan(x))

\frac{\partial}{\partial x} (sec (x) tan (x))

y^{^{'}} = 5 y^{\frac{1}{5}}

derivative of 3x+6/x

\frac{d}{d x} (3 x + \frac{6}{x})

derivative of 1/2 sin(x)

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

integral of (e^x-3)^4e^x

\int (e^{x} - 3)^{4} e^{x} d x

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(e^{-2t}cos(2x)) ?
The answer to (\partial)/(\partial x)(e^{-2t}cos(2x)) is -2e^{-2t}sin(2x)