Find the derivatives of the function. h(t)=\frac{t+1}{t^{2}+2t+2}

Falak Kinney

Falak Kinney

Answered question

2021-11-07

Find the derivatives of the function.
h(t)=t+1t2+2t+2

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-11-08Added 97 answers

h(t)=t+1t2+2t+2
Let
u=t+1, v=t2+2t+2
u'=1, v=2t21+2(1)+0
=2t+2
We know that,
(uv)=vuuvv2
Differentiating h with respect to t,
h(t)=(t+1t2+2t+2)
=(t2+2t+2)(1)(t+1)(2t+2)(t2+2t+2)2
=t2+2t+2(2t2+2t+2t+2)(t2+2t+2)2
=t2+2t+22t24t2(t2+2t+2)2
=t22t(t2+2t+2)2
=t(t+2)(t2+2t+2)2

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