Differentiate y = (4-3x) ^9 by chain rule
Answers
Answer:
nx=(n-1)
Explanation:
y=(4−3x)
9
dx
dy
=
dx
d
(4−3x)
9
dx
dy
=
dx
d
(4−3x)
9
×
dx
d
(4−3x)
As It is a Function of a Function!
Now differentiating :-
\begin{gathered}\frac{dy}{dx} = \frac{d}{dx} {(4 - 3x)}^{9} \times \frac{d}{dx}(4 - 3x) \\ \\ \\ \\ \frac{dy}{dx} = 9 {(4 - 3x)}^{9 - 1} \times ( \frac{d}{dx}4 - \frac{d}{dx}3x) \\ \\ \\ \frac{dy}{dx} = 9 {(4 - 3x)}^{8} \times (0 - 3) \\ \\ \\ \\ \frac{dy}{dx} = 9 {(4 - 3x)}^{8}( - 3) \\ \\ \\ \frac{dy}{dx} =(- 27 {(4 - 3x)}^{8})\end{gathered}
dx
dy
=
dx
d
(4−3x)
9
×
dx
d
(4−3x)
dx
dy
=9(4−3x)
9−1
×(
dx
d
4−
dx
d
3x)
dx
dy
=9(4−3x)
8
×(0−3)
dx
dy
=9(4−3x)
8
(−3)
dx
dy
=(−27(4−3x)
8
)
The general Formula used is :-
\begin{gathered}y = {x}^{n} \\ \\ \\ \frac{dy}{dx} = n {x}^{(n - 1)}\end{gathered}
y=x
n
dx
dy
=nx
(n−1)
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