Calculate the derivatives of the functions. t(x)=[(x+1)^{0.1}-4x]^{-5.1}

iohanetc

iohanetc

Answered question

2021-05-04

Calculate the derivatives of the functions. t(x)=[(x+1)0.14x]5.1

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-05-05Added 92 answers

Denote
u=(x+1)0.14x
Then
t(u)=u5.1
Now, recall the chain rule:
ddx[f(u)]=f(u)dudx
Using the chain rule, we get
ddx[t(u)]=(u5.1)dudx
=5.1u6.1dudx
=5.1((x+1)0.14x)6.1((x+1)0.14x)
=5.1((x+1)0.14x)6.1(0.1(x+1)0.9(1)4) }chain rule
=5.1((x+1)0.14x)6.1(0.1(x+1)0.94)

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