What is the derivative of 3^{2^{x^2}} ?

The derivative of 3^{2^{x^2}} is ln(3)ln(2)*3^{2^{x^2}}*2^{x^2+1}x

What is the first derivative of 3^{2^{x^2}} ?

The first derivative of 3^{2^{x^2}} is ln(3)ln(2)*3^{2^{x^2}}*2^{x^2+1}x

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derivative of

3^{2^{x^{2}}}

ln (3) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{x^{2} + 1} x

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{2^{x^{2}} l n (3)})

Apply the chain rule:

e^{2^{x^{2}} l n (3)} \frac{d}{d x} (2^{x^{2}} ln (3))

= e^{2^{x^{2}} l n (3)} \frac{d}{d x} (2^{x^{2}} ln (3))

\frac{d}{d x} (2^{x^{2}} ln (3)) = ln (3) ln (2) \cdot 2^{x^{2} + 1} x

= e^{2^{x^{2}} l n (3)} ln (3) ln (2) \cdot 2^{x^{2} + 1} x

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

= ln (3) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{x^{2} + 1} x

x \to 0 lim (\frac{sin ( x ^{7} )}{x})

x \to - 2 + lim (\frac{- 1}{x ^{2} - 4})

\int s 5^{s} d s

\frac{1}{x ^{3}}

sin (tan (2 x))

What is the derivative of 3^{2^{x^2}} ?
The derivative of 3^{2^{x^2}} is ln(3)ln(2)*3^{2^{x^2}}*2^{x^2+1}x
What is the first derivative of 3^{2^{x^2}} ?
The first derivative of 3^{2^{x^2}} is ln(3)ln(2)*3^{2^{x^2}}*2^{x^2+1}x