What is the derivative of 6^{-x} ?

The derivative of 6^{-x} is -ln(6)*6^{-x}

What is the first derivative of 6^{-x} ?

The first derivative of 6^{-x} is -ln(6)*6^{-x}

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\frac{d}{d x} (6^{- x})

- ln (6) \cdot 6^{- x}

Solution steps

\frac{d}{d x} (6^{- x})

Apply exponent rule:

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

6^{- x} = e^{(- x) l n (6)}

= \frac{d}{d x} (e^{(- x) l n (6)})

Apply the chain rule:

e^{(- x) l n (6)} \frac{d}{d x} ((- x) ln (6))

= e^{(- x) l n (6)} \frac{d}{d x} ((- x) ln (6))

\frac{d}{d x} ((- x) ln (6)) = - ln (6)

= e^{(- x) l n (6)} (- ln (6))

Simplify

e^{(- x) l n (6)} (- ln (6)) : - ln (6) \cdot 6^{- x}

= - ln (6) \cdot 6^{- x}

x^{3}

x \to 0 + lim (\frac{csc ( 2 x )}{x})

y^{^{''}} - y = 0, y (0) = 2

x + y = - 3, x + 9 = y^{2}

\frac{d}{d x} (cos (x - \frac{π}{2}))

What is the derivative of 6^{-x} ?
The derivative of 6^{-x} is -ln(6)*6^{-x}
What is the first derivative of 6^{-x} ?
The first derivative of 6^{-x} is -ln(6)*6^{-x}