13. Compute the derivatives of the following functions
(a) \( f(x)=6 e^{x^{4}+x^{2}} \)
(b) \( f(x)=\ln \left(x^{2}+1\right) \)

Answer

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Answer

\( = 6e^{x^{4}+x^{2}}(4x^{3}+2x) \)

Steps

Step 1 ：\( \frac{d}{dx}(6 e^{x^{4}+x^{2}}) = 6 \frac{d}{dx} (e^{x^{4}+x^{2}})\)

Step 2 ：\( = 6e^{x^{4}+x^{2}} \frac{d}{dx}(x^{4}+x^{2}) \)

Step 3 ：\( = 6e^{x^{4}+x^{2}}(4x^{3}+2x) \)