Get the solution to "Calculate the derivatives of the functions. t(x)=[(x+1)0.1−4x]−5.1" - Plainmath

iohanetc

Answered question

2021-05-04

Calculate the derivatives of the functions.

t (x) = {[{(x + 1)}^{0.1} - 4 x]}^{- 5.1}

Answer & Explanation

Adnaan Franks

Skilled2021-05-05Added 92 answers

Denote

u = {(x + 1)}^{0.1} - 4 x

Then

t (u) = u^{- 5.1}

Now, recall the chain rule:

\frac{d}{d x} [f (u)] = f^{'} (u) \frac{d u}{d x}

Using the chain rule, we get

\frac{d}{d x} [t (u)] = {(u^{- 5.1})}^{'} \frac{d u}{d x}

= - 5.1 u^{- 6.1} \frac{d u}{d x}

= - 5.1 {({(x + 1)}^{0.1} - 4 x)}^{- 6.1} {({(x + 1)}^{0.1} - 4 x)}^{'}

= - 5.1 {({(x + 1)}^{0.1} - 4 x)}^{- 6.1} (0.1 {(x + 1)}^{- 0.9} (1) - 4)

}chain rule

= - 5.1 {({(x + 1)}^{0.1} - 4 x)}^{- 6.1} (0.1 {(x + 1)}^{- 0.9} - 4)

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