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

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

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

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

- e^{- x} t^{4}

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= t^{4} e^{- x} (- 1)

Simplify

= - e^{- x} t^{4}

\int (\frac{2}{x} - 3 x x + 2) d x

y = - x^{3} + 2 x^{2} + 1, at x = - 1

y^{^{''}} - 2 a y^{^{'}} + a^{2} y = 0

\int - sin (θ) d θ

\int 3 t^{2} - 2 t d t

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