What is (\partial)/(\partial x)(t^2e^{(x^2)/(4t)}) ?

The answer to (\partial)/(\partial x)(t^2e^{(x^2)/(4t)}) is (e^{(x^2)/(4t)}tx)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(t^2e^{(x^2)/(4t)})

\frac{\partial}{\partial x} (t^{2} e^{\frac{x ^{2}}{4 t}})

\frac{e ^{\frac{x ^{2}}{4 t}} t x}{2}

Solution steps

\frac{\partial}{\partial x} (t^{2} e^{\frac{x ^{2}}{4 t}})

Treat

t

as a constant

Take the constant out:

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

= t^{2} \frac{\partial}{\partial x} (e^{\frac{x ^{2}}{4 t}})

Apply the chain rule:

e^{\frac{x ^{2}}{4 t}} \frac{\partial}{\partial x} (\frac{x ^{2}}{4 t})

= e^{\frac{x ^{2}}{4 t}} \frac{\partial}{\partial x} (\frac{x ^{2}}{4 t})

\frac{\partial}{\partial x} (\frac{x ^{2}}{4 t}) = \frac{x}{2 t}

= t^{2} e^{\frac{x ^{2}}{4 t}} \frac{x}{2 t}

Simplify

t^{2} e^{\frac{x ^{2}}{4 t}} \frac{x}{2 t} : \frac{e ^{\frac{x ^{2}}{4 t}} t x}{2}

= \frac{e ^{\frac{x ^{2}}{4 t}} t x}{2}

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

f (x) = - 64 x (- 16 x^{2} + 36)

(x^{2} - y^{2}) d x - 2 x y d y = 0

\frac{\partial}{\partial x} ((\frac{x}{y}) e^{x y})

\int 5 x cos (2 x) d x

What is (\partial)/(\partial x)(t^2e^{(x^2)/(4t)}) ?
The answer to (\partial)/(\partial x)(t^2e^{(x^2)/(4t)}) is (e^{(x^2)/(4t)}tx)/2