What is the derivative of y=8^{4^{x^2}} ?

The derivative of y=8^{4^{x^2}} is 3ln^2(2)*2^{3*4^{x^2}+2x^2+2}x

What is the first derivative of y=8^{4^{x^2}} ?

The first derivative of y=8^{4^{x^2}} is 3ln^2(2)*2^{3*4^{x^2}+2x^2+2}x

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derivative of

y = 8^{4^{x^{2}}}

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

Solution steps

\frac{d}{d x} (8^{4^{x^{2}}})

Apply exponent rule:

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

8^{4^{x^{2}}} = e^{4^{x^{2}} l n (8)}

= \frac{d}{d x} (e^{4^{x^{2}} l n (8)})

Apply the chain rule:

e^{4^{x^{2}} l n (8)} \frac{d}{d x} (4^{x^{2}} ln (8))

= e^{4^{x^{2}} l n (8)} \frac{d}{d x} (4^{x^{2}} ln (8))

\frac{d}{d x} (4^{x^{2}} ln (8)) = 3 ln^{2} (2) \cdot 2^{2 x^{2} + 2} x

= e^{4^{x^{2}} l n (8)} \cdot 3 ln^{2} (2) \cdot 2^{2 x^{2} + 2} x

Simplify

e^{4^{x^{2}} l n (8)} \cdot 3 ln^{2} (2) \cdot 2^{2 x^{2} + 2} x : 3 ln^{2} (2) \cdot 2^{3 \cdot 4^{x^{2}} + 2 x^{2} + 2} x

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

What is the derivative of y=8^{4^{x^2}} ?
The derivative of y=8^{4^{x^2}} is 3ln^2(2)*2^{3*4^{x^2}+2x^2+2}x
What is the first derivative of y=8^{4^{x^2}} ?
The first derivative of y=8^{4^{x^2}} is 3ln^2(2)*2^{3*4^{x^2}+2x^2+2}x