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Step-by-step Solution

Derive the function sin(2*((1-1*ln(x))/x)) with respect to x

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Answer

$-x\frac{1}{x}$

Step-by-step explanation

Problem to solve:

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

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

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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

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Answer

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

Main topic:

Differential calculus

Used formulas:

7. See formulas

Time to solve it:

~ 2.89 seconds

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