What is the derivative of $y = 2^{3^{x^{2}}}$ using the chain rule?
Please show step by step solution.
What is the derivative of $y = 2^{3^{x^{2}}}$ using the chain rule?
Please show step by step solution.
$y = 2^{3^{x^{2}}}$
$y' = 2^{3^{x^{2}}}\ln2 (3^{x^{2}})'$
$y' = 2^{3^{x^{2}}}\ln2 (3^{x^{2}}\ln3)(x^2)'$
$y' = 2^{3^{x^{2}}}\ln2 (3^{x^{2}}\ln3)2x$
$y' = 2x\ln2 \ln3 2^{3^{x^{2}}}(3^{x^{2}})$
$y' = 2^{3^{x^{2}}}3^{x^{2}}2x\ln3\ln2 $
Hint: for a function $a^u$, $\frac{d}{du} = a^u \ln a \cdot u'$
In your case, $a=2, u = 3^{x^2}$.