zi2lalZ

2021-10-14

Use the rules for derivatives to find the derivative of function defined as follows.

$y=\sqrt{2{t}^{7}-5}$

ottcomn

Skilled2021-10-15Added 97 answers

Step 1

The given function is,

$y=\sqrt{2{t}^{7}-5}$

To find the derivative of the given function, we use the chain rule of derivative,

${f}^{\prime}\left(x\right)=\frac{d}{d\left(g\left(x\right)\right)}\left(f\left(x\right)\right)\cdot \frac{d}{dx}\left(g\left(x\right)\right)$

Applying the chain rule of derivative, we get

$y}^{\prime}=\frac{dy}{dt$

$=\frac{d}{dt}\left(\sqrt{2{t}^{7}-5}\right)$

$=\frac{d}{d(2{t}^{7}-5)}\left(\sqrt{2{t}^{7}-5}\right)\cdot \frac{d}{dt}(2{t}^{7}-5)$

Step 2

To solve further, we use the power rule of differentiation,$\frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}$

${y}^{\prime}=\frac{d}{d(2{t}^{7}-5)}\left(\sqrt{2{t}^{7}-5}\right)\cdot \frac{d}{dt}(2{t}^{7}-5)$

$=\left(\frac{1}{2\sqrt{2{t}^{7}-5}}\right)\cdot (2\left(7{t}^{6}\right)-0)$

$=\frac{7{t}^{6}}{\sqrt{2{t}^{7}-5}}$

Therefore, the derivative of the given function is$\frac{7{t}^{6}}{\sqrt{2{t}^{7}-5}}$

The given function is,

To find the derivative of the given function, we use the chain rule of derivative,

Applying the chain rule of derivative, we get

Step 2

To solve further, we use the power rule of differentiation,

Therefore, the derivative of the given function is

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