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

Answer

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Answer

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

Steps

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

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

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