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2 years ago

(x-1)³ find derivative using definition

Mathematics

2 answers:

Neko [114]2 years ago

5 0

Answer:

f'(x) = 3(x−1)²

Step-by-step explanation:

Definition of derivative is:

f'(x) = lim(h→0) [f(x + h) − f(x)] / h

f(x) = (x−1)³, so the derivative is:

f'(x) = lim(h→0) [(x−1+h)³ − (x−1)³] / h

f'(x) = lim(h→0) [(x−1)³ + 3(x−1)²h + 3(x−1)h² + h³ − (x−1)³] / h

f'(x) = lim(h→0) [3(x−1)²h + 3(x−1)h² + h³] / h

f'(x) = lim(h→0) [3(x−1)² + 3(x−1)h + h²]

f'(x) = 3(x−1)²

kakasveta [241]2 years ago

3 0

Step-by-step explanation:

definition of the derivative to differentiate functions. This tutorial is well understood if used with the difference quotient .

The derivative f ' of function f is defined ascthe above pic.

when this limit exists. Hence, to find the derivative from its definition, we need to find the limit of the difference quotient.

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ArbitrLikvidat [17]

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the answer Part R is

$14-----> R$

Part Y) $3(2x+9)=6x+$

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the answer Part Y is

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$8(3x+1)=24x+8$

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the answer Part S is

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$a(4+b)=4a+ab$

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the answer Part O is

$17-----> O$

Part E) $x(y+10)=+10x$

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the answer Part E is

$3-----> E$

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Using the distributive property

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the answer Part I is

$20-----> I$

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the answer Part D is

$10-----> D$

Part W) $x(a+3b)=+3bx$

Using the distributive property

$x(a+3b)=ax+3bx$

therefore

the answer Part W is

$18-----> W$

Part E) $a(8x+2y)=8ax+$

Using the distributive property

$a(8x+2y)=8ax+2ay$

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the answer Part E is

$7-----> E$

Part T) $0.5(4a+10)=2a+$

Using the distributive property

Part T) $0.5(4a+10)=2a+5$

therefore

the answer Part T is

$1-----> T$

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the answer Part R is

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the answer Part O is

$13-----> O$

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the answer Part T is

$22-----> T$

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the answer Part H is

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the answer Part A is

$5-----> A$

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$(2/5)m+(2/5)n=(2/5)(m+n)$

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$12-----> F$

Part M) $(3/4)a+(3/4)b+(3/4)c=\ (a+b+c)$

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A coordinate point is always in the form (x,y) that means the first point is always x-coordinate and the second point is always y-coordinate.

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(x-1)³ find derivative using definition​

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