Question

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

Answer 1

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 :

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

Answer 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