What is the derivative of 10^{9-x^2} ?

The derivative of 10^{9-x^2} is -ln(10)*5^{9-x^2}*2^{-x^2+10}x

What is the first derivative of 10^{9-x^2} ?

The first derivative of 10^{9-x^2} is -ln(10)*5^{9-x^2}*2^{-x^2+10}x

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\frac{d}{d x} (1 0^{9 - x^{2}})

- ln (10) \cdot 5^{9 - x^{2}} \cdot 2^{- x^{2} + 10} x

Solution steps

\frac{d}{d x} (1 0^{9 - x^{2}})

Apply exponent rule:

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

1 0^{9 - x^{2}} = e^{(9 - x^{2}) l n (10)}

= \frac{d}{d x} (e^{(9 - x^{2}) l n (10)})

Apply the chain rule:

e^{(9 - x^{2}) l n (10)} \frac{d}{d x} ((9 - x^{2}) ln (10))

= e^{(9 - x^{2}) l n (10)} \frac{d}{d x} ((9 - x^{2}) ln (10))

\frac{d}{d x} ((9 - x^{2}) ln (10)) = - 2 ln (10) x

= e^{(9 - x^{2}) l n (10)} (- 2 ln (10) x)

Simplify

e^{(9 - x^{2}) l n (10)} (- 2 ln (10) x) : - ln (10) \cdot 5^{9 - x^{2}} \cdot 2^{- x^{2} + 10} x

= - ln (10) \cdot 5^{9 - x^{2}} \cdot 2^{- x^{2} + 10} x

t^{2} sin (2 t)

x y^{^{'}} = y + 4 x^{2} sin (x), y (π) = 0

(1 + x^{2}) \frac{d y}{d x} = \frac{x ^{1}}{y}

\frac{d}{d x} (x^{4} - 13 x^{2} + 36)

∣ x ∣, 4 - x^{2}

What is the derivative of 10^{9-x^2} ?
The derivative of 10^{9-x^2} is -ln(10)*5^{9-x^2}*2^{-x^2+10}x
What is the first derivative of 10^{9-x^2} ?
The first derivative of 10^{9-x^2} is -ln(10)*5^{9-x^2}*2^{-x^2+10}x