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# Find the derivative of $\sin\left(8x^2-1\right)^2$

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##  Final answer to the problem

$32x\sin\left(8x^2-1\right)\cos\left(8x^2-1\right)$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Find the derivative using the definition
• Find the derivative using the product rule
• Find the derivative using the quotient rule
• Find the derivative using logarithmic differentiation
• Find the derivative
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
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1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2\sin\left(8x^2-1\right)^{1}\frac{d}{dx}\left(\sin\left(8x^2-1\right)\right)$

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$2\sin\left(8x^2-1\right)^{1}\frac{d}{dx}\left(\sin\left(8x^2-1\right)\right)$

Learn how to solve problems step by step online. Find the derivative of sin(8x^2-1)^2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Any expression to the power of 1 is equal to that same expression. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

##  Final answer to the problem

$32x\sin\left(8x^2-1\right)\cos\left(8x^2-1\right)$

##  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

SnapXam A2

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0
a
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u
v
w
x
y
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.
(◻)
+
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◻/◻
/
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
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