Derivatives Evaluate the following derivatives. ddt(t1t)

Joseph Krupa

Joseph Krupa

Answered

2022-01-15

Derivatives Evaluate the following derivatives.
ddt(t1t)

Answer & Explanation

Thomas White

Thomas White

Expert

2022-01-16Added 40 answers

Step 1
To evaluate
ddt(t1t)
Step 2
Let y=t1t
Taking logarithm on both sides
ln(y)=ln(t1t)
ln(y)=1tln(t)
Differentiate both sides with respect to t
1ydydt=(1t)ln(t)+(1t)[ln(t)]
dydt=y[1t2ln(t)+1t×1t]
dydt=y[1t2ln(t)+1t2]
ddt(t1t)=(t1t)[1t2(1ln(t))]
Lakisha Archer

Lakisha Archer

Expert

2022-01-17Added 39 answers

(t1t)=[(elnt)1t]=(e(1t)lnt)=
=e(1t)lnt(1tlnt)=
=e(1t)lnt(1t2lnt+1t1t)=
=t1t1t2(lnt+1)
=t(1t)2(1lnt)
Result:
t(1t)2(1lnt)

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