Math, asked by mondalmonir3846, 9 months ago

Find the derivative of f(x) = 8 divided by x at x = -1.

Answers

Answered by kaushik05
11

To find :

Derivative of f(x)=8/x at x= -1

Solution:

f(x) =  y = \frac{8}{x}

Differentiate w.r.t x , we get :

 \implies \:  \frac{dy}{dx}  =  \frac{d}{dx}  \frac{8}{x}  \\  \\  \implies \:  \frac{dy}{dx}  = 8 \:  \frac{d}{dx}  \frac{1}{x}  \\  \\  \implies \:  \frac{dy}{dx}  = 8 \frac{d}{dx}  {x}^{ - 1}  \\  \\  \implies \:  \frac{dy}{dx}  = 8( - 1) {x}^{ - 1 - 1}  \\  \\  \implies \:  \frac{dy}{dx}  =  \frac{ - 8}{ {x}^{2} }

•At x=-1

 \leadsto \:  \frac{dy}{dx}  =  \frac{ - 8}{ { - 1}^{2} }  \\  \\  \leadsto \:  \frac{dy}{dx}  =  - 8

Formula :

 \star \boxed{  \red{\frac{d}{dx}  {x}^{n}  = n {x}^{n - 1} }}

Answered by XxROMEOxX
2

Step-by-step explanation:

To find :

• Derivative of f(x)=8/x at x= -1

Solution:

f(x) = y = \frac{8}{x}f(x)=y=

x

8

Differentiate w.r.t x , we get :

\begin{gathered}\implies \: \frac{dy}{dx} = \frac{d}{dx} \frac{8}{x} \\ \\ \implies \: \frac{dy}{dx} = 8 \: \frac{d}{dx} \frac{1}{x} \\ \\ \implies \: \frac{dy}{dx} = 8 \frac{d}{dx} {x}^{ - 1} \\ \\ \implies \: \frac{dy}{dx} = 8( - 1) {x}^{ - 1 - 1} \\ \\ \implies \: \frac{dy}{dx} = \frac{ - 8}{ {x}^{2} }\end{gathered}

dx

dy

=

dx

d

x

8

dx

dy

=8

dx

d

x

1

dx

dy

=8

dx

d

x

−1

dx

dy

=8(−1)x

−1−1

dx

dy

=

x

2

−8

•At x=-1

\begin{gathered}\leadsto \: \frac{dy}{dx} = \frac{ - 8}{ { - 1}^{2} } \\ \\ \leadsto \: \frac{dy}{dx} = - 8\end{gathered}

dx

dy

=

−1

2

−8

dx

dy

=−8

Formula :

\star \boxed{ \red{\frac{d}{dx} {x}^{n} = n {x}^{n - 1} }}⋆

dx

d

x

n

=nx

n−1

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