Write an example of a function and solve whose derivative can be found by using the following rules: a) Product rule and special function differentiation rules b) Power rule, quotient rule, and chain rule c) Chain rule twice d) Implicit differentiation and special function differentiation rule I am attaching example use another examples but solution liek that
Write an example of a function and solve whose derivative can be found by using the following rules: a) Product rule and special function differentiation rules b) Power rule, quotient rule, and chain rule c) Chain rule twice d) Implicit differentiation and special function differentiation rule I am attaching example use another examples but solution liek that
Write an example of a function and solve whose derivative can be found by using the following rules: a) Product rule and special function differentiation rules b) Power rule, quotient rule, and chain rule c) Chain rule twice d) Implicit differentiation and special function differentiation rule I am attaching example use another examples but solution liek that
Write an example of a function and solve whose derivative can be found by using the following rules:
a) Product rule and special function differentiation rules
b) Power rule, quotient rule, and chain rule
c) Chain rule twice
d) Implicit differentiation and special function differentiation rule
I am attaching example use another examples but solution liek that
Transcribed Image Text:(a) PRODUCT RULE EXAMPLES:
f(x) = (3x²+4) (2x³-3x)
f'(X) = (3x² + 4) £x (2x³ =3x) + x ( 3X²+4) (2x³-3x)
d/dx (2x³-3x) = 6x² 3! (3x²+4) =GX
f'(x) = (3x²+4) (GX²-3) + (GX) (RX³-3x)
18x4-9x2 + 24x² -12 +12x" -18x²
[ƒ¹(x) = 30 x² - 3X²-/2
PUNCTION
SPECIAL A DIFFERENTIAL RULES:
LOENTITIES
d
dx
d
dx
d
ax
d
dx
G=0
n
*²
ex.
x
=e
n-l
Tin XECOSX
COS X = SHAX
b) POWER RULE.
f(x) = x²
f'(x) = 2x²
f(x)=2x
2+
EXAMPLES
QUOTIENT RULE:
f(x)= x² + 3x
xf4
|f'(x)=
dt
(ssint + 8cust)
& (5 sint) + & (&cost)
at
50 sint
+ &at cust
Scost
= 5cost
f'(x) = (x+4) (2x+3) - (X+9x) (1)
(x+4)²
2x+3x18x+12-X-3X
2
(x+4)
x² 18x+12
+-8 sint
(x+4)2
(x+2)(x+4)
(x+4)2
-ssin t
CHAIN RULT:
f(x) = (x²+1) ³
f'(x) = 3 (x²+1
f'(x) = 6x (x²+
Formula Formula d d x f g = g × d d x f - f × d d x g g 2 , i f g ≠ 0
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