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Find the derivative of $\left(\sin\left(7x-2\right)^3\right)^4$

Step-by-step Solution

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Solution

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Final Answer

$84\sin\left(7x-2\right)^{11}\cos\left(7x-2\right)$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\left(\sin\left(7x-2\right)^3\right)^4\right)$

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1

Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\sin\left(7x-2\right)^{12}\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(\sin\left(7x-2\right)^{12}\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of sin(7x-2)^3^4. Simplify the derivative by applying the properties of logarithms. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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

$84\sin\left(7x-2\right)^{11}\cos\left(7x-2\right)$

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

Find the derivativeFind derivative of sin(7x-2)^3^4 using the product ruleFind derivative of sin(7x-2)^3^4 using the quotient ruleFind derivative of sin(7x-2)^3^4 using logarithmic differentiationFind derivative of sin(7x-2)^3^4 using the definition

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a
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(◻)
+
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×
◻/◻
/
÷
◻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

How to improve your answer:

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Main topic:

Differential Calculus

Used formulas:

6. See formulas

Related topics:

Differential CalculusCalculusPower Rule for DerivativesBasic Differentiation RulesSum Rule of DifferentiationConstant Rule for Differentiation

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