What is (\partial)/(\partial x)(e^{-6t}(x+3t)) ?

The answer to (\partial)/(\partial x)(e^{-6t}(x+3t)) is e^{-6t}

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(\partial)/(\partial x)(e^{-6t}(x+3t))

\frac{\partial}{\partial x} (e^{- 6 t} (x + 3 t))

e^{- 6 t}

Solution steps

\frac{\partial}{\partial x} (e^{- 6 t} (x + 3 t))

Treat

t

as a constant

Take the constant out:

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

= e^{- 6 t} \frac{\partial}{\partial x} (x + 3 t)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= e^{- 6 t} (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (3 t))

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

\frac{\partial}{\partial x} (3 t) = 0

= e^{- 6 t} (1 + 0)

Simplify

= e^{- 6 t}

\frac{d ^{2}}{d x ^{2}} (\frac{4 x ^{3} + 6}{x})

\frac{s}{s ^{2} - 4 s + 5}

\int_{t}^{2} \frac{1}{x - 1} d x

\frac{d}{d x} (- (\frac{1}{x}))

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

What is (\partial)/(\partial x)(e^{-6t}(x+3t)) ?
The answer to (\partial)/(\partial x)(e^{-6t}(x+3t)) is e^{-6t}