What is the derivative of 3^{-x} ?

The derivative of 3^{-x} is -ln(3)*3^{-x}

What is the first derivative of 3^{-x} ?

The first derivative of 3^{-x} is -ln(3)*3^{-x}

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derivative of

3^{- x}

- ln (3) \cdot 3^{- x}

Solution steps

\frac{d}{d x} (3^{- x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

3^{- x} = e^{(- x) l n (3)}

= \frac{d}{d x} (e^{(- x) l n (3)})

Apply the chain rule:

e^{(- x) l n (3)} \frac{d}{d x} ((- x) ln (3))

= e^{(- x) l n (3)} \frac{d}{d x} ((- x) ln (3))

\frac{d}{d x} ((- x) ln (3)) = - ln (3)

= e^{(- x) l n (3)} (- ln (3))

Simplify

e^{(- x) l n (3)} (- ln (3)) : - ln (3) \cdot 3^{- x}

= - ln (3) \cdot 3^{- x}

x \to 6 lim (- x^{2} + 4 x - 3)

\int csc (x) sec^{2} (x) d x

\int \frac{x ^{2} + 1}{x ^{2} - 5 x + 6} d x

\frac{\partial}{\partial x} (5 e^{2 x})

y = \frac{x ^{4}}{4} + \frac{2}{9} x^{3} - x^{2} + 9 x - 5

What is the derivative of 3^{-x} ?
The derivative of 3^{-x} is -ln(3)*3^{-x}
What is the first derivative of 3^{-x} ?
The first derivative of 3^{-x} is -ln(3)*3^{-x}