What is the derivative of 1/(3^x) ?

The derivative of 1/(3^x) is -ln(3)*3^{-x}

What is the first derivative of 1/(3^x) ?

The first derivative of 1/(3^x) is -ln(3)*3^{-x}

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derivative of

\frac{1}{3 ^{x}}

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

Solution steps

\frac{d}{d x} (\frac{1}{3 ^{x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \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}

f (x) = \frac{x ^{2} - 1}{2 x + 2}

f (x) = 4 x^{4} - 5 x^{3} + 2 x - 3

\frac{d}{d x} (\frac{x}{a ^{2} a ^{2} + x ^{2}})

\frac{d}{d x} (25 ln (x^{2}) - x^{2})

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 4)^{5})

What is the derivative of 1/(3^x) ?
The derivative of 1/(3^x) is -ln(3)*3^{-x}
What is the first derivative of 1/(3^x) ?
The first derivative of 1/(3^x) is -ln(3)*3^{-x}