What is the derivative of 10^{-2x} ?

The derivative of 10^{-2x} is -ln(10)*25^{-x}*2^{-2x+1}

What is the first derivative of 10^{-2x} ?

The first derivative of 10^{-2x} is -ln(10)*25^{-x}*2^{-2x+1}

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\frac{d}{d x} (1 0^{- 2 x})

- ln (10) \cdot 2 5^{- x} \cdot 2^{- 2 x + 1}

Solution steps

\frac{d}{d x} (1 0^{- 2 x})

Simplify

1 0^{- 2 x} : 10 0^{- x}

= \frac{d}{d x} (10 0^{- x})

Apply exponent rule:

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

10 0^{- x} = e^{(- x) l n (100)}

= \frac{d}{d x} (e^{(- x) l n (100)})

Apply the chain rule:

e^{(- x) l n (100)} \frac{d}{d x} ((- x) ln (100))

= e^{(- x) l n (100)} \frac{d}{d x} ((- x) ln (100))

\frac{d}{d x} ((- x) ln (100)) = - 2 ln (10)

= e^{(- x) l n (100)} (- 2 ln (10))

Simplify

e^{(- x) l n (100)} (- 2 ln (10)) : - ln (10) \cdot 2 5^{- x} \cdot 2^{- 2 x + 1}

= - ln (10) \cdot 2 5^{- x} \cdot 2^{- 2 x + 1}

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

\frac{8}{( 9 s ^{2} + 12 s + 4 ) ( s )}

\int x \cdot e^{x^{2}} d x

\frac{d ^{2} x}{d t ^{2}} + 9 x = - sin (3 t)

\frac{\partial}{\partial x} (ln (\frac{2 x y}{z}))

What is the derivative of 10^{-2x} ?
The derivative of 10^{-2x} is -ln(10)*25^{-x}*2^{-2x+1}
What is the first derivative of 10^{-2x} ?
The first derivative of 10^{-2x} is -ln(10)*25^{-x}*2^{-2x+1}