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Popular >

derivative of 2^{(2-x^4})

Solution

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

Solution

- ln (2) \cdot 2^{- x^{4} + 4} x^{3}

Solution steps

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

Apply exponent rule:

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

2^{2 - x^{4}} = e^{(2 - x^{4}) l n (2)}

= \frac{d}{d x} (e^{(2 - x^{4}) l n (2)})

Apply the chain rule:

e^{(2 - x^{4}) l n (2)} \frac{d}{d x} ((2 - x^{4}) ln (2))

= e^{(2 - x^{4}) l n (2)} \frac{d}{d x} ((2 - x^{4}) ln (2))

\frac{d}{d x} ((2 - x^{4}) ln (2)) = - 4 ln (2) x^{3}

= e^{(2 - x^{4}) l n (2)} (- 4 ln (2) x^{3})

Simplify

e^{(2 - x^{4}) l n (2)} (- 4 ln (2) x^{3}) : - ln (2) \cdot 2^{- x^{4} + 4} x^{3}

= - ln (2) \cdot 2^{- x^{4} + 4} x^{3}

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Frequently Asked Questions (FAQ)

What is the derivative of 2^{(2-x^4}) ?
The derivative of 2^{(2-x^4}) is -ln(2)*2^{-x^4+4}x^3
What is the first derivative of 2^{(2-x^4}) ?
The first derivative of 2^{(2-x^4}) is -ln(2)*2^{-x^4+4}x^3