What is the derivative of 10^{-3x^2} ?

The derivative of 10^{-3x^2} is -3ln(10)*125^{-x^2}*2^{-3x^2+1}x

What is the first derivative of 10^{-3x^2} ?

The first derivative of 10^{-3x^2} is -3ln(10)*125^{-x^2}*2^{-3x^2+1}x

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\frac{d}{d x} (1 0^{- 3 x^{2}})

- 3 ln (10) \cdot 12 5^{- x^{2}} \cdot 2^{- 3 x^{2} + 1} x

Solution steps

\frac{d}{d x} (1 0^{- 3 x^{2}})

Simplify

1 0^{- 3 x^{2}} : 100 0^{- x^{2}}

= \frac{d}{d x} (100 0^{- x^{2}})

Apply exponent rule:

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

100 0^{- x^{2}} = e^{(- x^{2}) l n (1000)}

= \frac{d}{d x} (e^{(- x^{2}) l n (1000)})

Apply the chain rule:

e^{(- x^{2}) l n (1000)} \frac{d}{d x} ((- x^{2}) ln (1000))

= e^{(- x^{2}) l n (1000)} \frac{d}{d x} ((- x^{2}) ln (1000))

\frac{d}{d x} ((- x^{2}) ln (1000)) = - 6 ln (10) x

= e^{(- x^{2}) l n (1000)} (- 6 ln (10) x)

Simplify

e^{(- x^{2}) l n (1000)} (- 6 ln (10) x) : - 3 ln (10) \cdot 12 5^{- x^{2}} \cdot 2^{- 3 x^{2} + 1} x

= - 3 ln (10) \cdot 12 5^{- x^{2}} \cdot 2^{- 3 x^{2} + 1} x

\int x^{2} + 49 d x

y = 2 x, y = \frac{2 x}{3}

\frac{d}{d x} (2 x + y)^{3} = x

\frac{\partial}{\partial x} (cos^{3} (x))

\int \frac{x + 16}{x} d x

What is the derivative of 10^{-3x^2} ?
The derivative of 10^{-3x^2} is -3ln(10)*125^{-x^2}*2^{-3x^2+1}x
What is the first derivative of 10^{-3x^2} ?
The first derivative of 10^{-3x^2} is -3ln(10)*125^{-x^2}*2^{-3x^2+1}x