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Find the higher order ($3$) derivative of $2x^4+x^3+\sqrt{x-1}$

Step-by-step Solution

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Solution

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Final Answer

$48x+6+\frac{3}{8\sqrt{\left(x-1\right)^{5}}}$
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Step-by-step Solution

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Find the ($1$) derivative

$8x^{3}+3x^{2}+\frac{1}{2}\left(x-1\right)^{-\frac{1}{2}}$

Learn how to solve limits by direct substitution problems step by step online.

$8x^{3}+3x^{2}+\frac{1}{2}\left(x-1\right)^{-\frac{1}{2}}$

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Learn how to solve limits by direct substitution problems step by step online. Find the higher order (3) derivative of 2x^4+x^3(x-1)^1/2. Find the (1) derivative. Find the (2) derivative. Find the (3) derivative. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

Final Answer

$48x+6+\frac{3}{8\sqrt{\left(x-1\right)^{5}}}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of (2x^4+x^3) using the product ruleFind derivative of (2x^4+x^3) using the quotient ruleFind derivative of (2x^4+x^3) using logarithmic differentiationFind derivative of (2x^4+x^3) using the definition

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Function Plot

Plotting: $48x+6+\frac{3}{8\sqrt{\left(x-1\right)^{5}}}$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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