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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

2^{8 - x^{2}}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{4 x ^{2} + 2} d x

n = 0 \sum \infty \frac{( n ^{n} )}{n !}

\int \frac{1}{z} d z

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

(- 8.2) (- 10.5)

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