What is the derivative of (2+sin(x)/x) ?

The derivative of (2+sin(x)/x) is (xcos(x)-2-sin(x))/(x^2)

What is the first derivative of (2+sin(x)/x) ?

The first derivative of (2+sin(x)/x) is (xcos(x)-2-sin(x))/(x^2)

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\frac{d}{d x} (\frac{2 + sin ( x )}{x})

\frac{x cos ( x ) - 2 - sin ( x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 + sin ( x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 + sin ( x ) ) x - \frac{d x}{d x} ( 2 + sin ( x ) )}{x ^{2}}

\frac{d}{d x} (2 + sin (x)) = cos (x)

\frac{d x}{d x} = 1

= \frac{cos ( x ) x - 1 \cdot ( 2 + sin ( x ) )}{x ^{2}}

Simplify

\frac{cos ( x ) x - 1 \cdot ( 2 + sin ( x ) )}{x ^{2}} : \frac{x cos ( x ) - 2 - sin ( x )}{x ^{2}}

= \frac{x cos ( x ) - 2 - sin ( x )}{x ^{2}}

f (x) = 2 x^{3} - 5 x, at x = - 1

\frac{1}{( t ^{5} + 4 ) ^{4}}

\frac{d}{d x} (- ln (x - 2))

\int \frac{( x ^{2} - x + 8 )}{x ^{3} + 2 x} d x

6 t (\frac{d y}{d t}) + 5 y = t

What is the derivative of (2+sin(x)/x) ?
The derivative of (2+sin(x)/x) is (xcos(x)-2-sin(x))/(x^2)
What is the first derivative of (2+sin(x)/x) ?
The first derivative of (2+sin(x)/x) is (xcos(x)-2-sin(x))/(x^2)