Can anyone guide me how to differentiate this?
$$5^{{x}^{2}}$$
#Differentiation
bronze juniper
dawn flaxBOT
Can anyone guide me how to differentiate this?
$$5^{{x}^{2}}$$
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placid heartBOT
Kenny
torpid nexus
Can anyone guide me how to differentiate this?
$$5^{{x}^{2}}$$
Notice that $\exp(\ln(x))=x$.
torpid nexus
From there, use chain rule.
bronze juniper
$$e^{ln(5)x^{2}} $$
placid heartBOT
Kenny
bronze juniper
$(e^u)' = e^u \cdot u'$
torpid nexus
$$e^{ln(5)x^{2}} $$
Good, now just use chain rule when differntiating.
Eh, $\dv{x}e^u$ on the left.
placid heartBOT
Kocher
placid heartBOT
Kenny
bronze juniper
So $(e^{ln(5)x^{2}})' = e^{ln(5)x^{2}} \cdot (ln(5)x^{2})'$
placid heartBOT
Kenny
bronze juniper
$e^{ln(5)x^{2}} \cdot 2ln(5)x$
placid heartBOT
Kenny
tight swallow
Yes.
torpid nexus
$e^{ln(5)x^{2}} \cdot 2ln(5)x$
Good!
Now, obviously, you can simplify the first term back into its original form, but you got it.
And sorry, I had class.
plucky sinewBOT
@bronze juniper