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\frac{d}{dx}\left(\sin\left(2\frac{1-\ln\left(x\right)}{x}\right)\right)

Find the derivative of sin(2(1-1ln(x))/x)

Answer

$2\left(1-2\sin\left(\frac{1-\ln\left(x\right)}{x}\right)^2\right)\frac{-1-\left(1-\ln\left(x\right)\right)}{x^2}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\sin\left(2\frac{1-\ln\left(x\right)}{x}\right)\right)$
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 ${f'(x) = \cos(x)\cdot D_x(x)}$

$\frac{d}{dx}\left(2\frac{1-\ln\left(x\right)}{x}\right)\cos\left(2\frac{1-\ln\left(x\right)}{x}\right)$

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Answer

$2\left(1-2\sin\left(\frac{1-\ln\left(x\right)}{x}\right)^2\right)\frac{-1-\left(1-\ln\left(x\right)\right)}{x^2}$

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

Main topic:

Differential calculus

Used formulas:

6. See formulas

Time to solve it:

~ 0.42 seconds