What is (\partial)/(\partial x)(Ae^{-3x}) ?

The answer to (\partial)/(\partial x)(Ae^{-3x}) is -3Ae^{-3x}

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(\partial)/(\partial x)(Ae^{-3x})

\frac{\partial}{\partial x} (A e^{- 3 x})

- 3 A e^{- 3 x}

Solution steps

\frac{\partial}{\partial x} (A e^{- 3 x})

Take the constant out:

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

= A \frac{\partial}{\partial x} (e^{- 3 x})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- 3 x) = - 3

= A e^{- 3 x} (- 3)

Simplify

= - 3 A e^{- 3 x}

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 1, y^{^{'}} (0) = - 5

f (x) = arccos (e^{2 x})

x^{3} - 8 x^{2} + 12 x, - x^{3} + 8 x^{2} - 12 x

y = \frac{7}{( 1 - x ^{2} ) ^{3}}

\frac{\partial}{\partial x} (\frac{1}{x ^{4}})

What is (\partial)/(\partial x)(Ae^{-3x}) ?
The answer to (\partial)/(\partial x)(Ae^{-3x}) is -3Ae^{-3x}