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, $a=2, u = 3^{x^2}$.