What is the derivative of 10^{8-x^2} ?

The derivative of 10^{8-x^2} is -ln(10)*5^{8-x^2}*2^{-x^2+9}x

What is the first derivative of 10^{8-x^2} ?

The first derivative of 10^{8-x^2} is -ln(10)*5^{8-x^2}*2^{-x^2+9}x

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derivative of

1 0^{8 - x^{2}}

- ln (10) \cdot 5^{8 - x^{2}} \cdot 2^{- x^{2} + 9} x

Solution steps

\frac{d}{d x} (1 0^{8 - x^{2}})

Apply exponent rule:

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

1 0^{8 - x^{2}} = e^{(8 - x^{2}) l n (10)}

= \frac{d}{d x} (e^{(8 - x^{2}) l n (10)})

Apply the chain rule:

e^{(8 - x^{2}) l n (10)} \frac{d}{d x} ((8 - x^{2}) ln (10))

= e^{(8 - x^{2}) l n (10)} \frac{d}{d x} ((8 - x^{2}) ln (10))

\frac{d}{d x} ((8 - x^{2}) ln (10)) = - 2 ln (10) x

= e^{(8 - x^{2}) l n (10)} (- 2 ln (10) x)

Simplify

e^{(8 - x^{2}) l n (10)} (- 2 ln (10) x) : - ln (10) \cdot 5^{8 - x^{2}} \cdot 2^{- x^{2} + 9} x

= - ln (10) \cdot 5^{8 - x^{2}} \cdot 2^{- x^{2} + 9} x

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

\frac{d y}{d x} = \frac{7 x}{4 y}

\int \frac{3}{cos ^{2} ( x )} d x

\frac{\partial}{\partial s} (\frac{3 r + s}{t})

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 0

What is the derivative of 10^{8-x^2} ?
The derivative of 10^{8-x^2} is -ln(10)*5^{8-x^2}*2^{-x^2+9}x
What is the first derivative of 10^{8-x^2} ?
The first derivative of 10^{8-x^2} is -ln(10)*5^{8-x^2}*2^{-x^2+9}x