What is the derivative of 3(cos(x)ln(x)+(sin(x))/x) ?

The derivative of 3(cos(x)ln(x)+(sin(x))/x) is (3(2xcos(x)-sin(x)-x^2sin(x)ln(x)))/(x^2)

What is the first derivative of 3(cos(x)ln(x)+(sin(x))/x) ?

The first derivative of 3(cos(x)ln(x)+(sin(x))/x) is (3(2xcos(x)-sin(x)-x^2sin(x)ln(x)))/(x^2)

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derivative of

3 (cos (x) ln (x) + \frac{sin ( x )}{x})

\frac{3 ( 2 x cos ( x ) - sin ( x ) - x ^{2} sin ( x ) ln ( x ) )}{x ^{2}}

Solution steps

\frac{d}{d x} (3 (cos (x) ln (x) + \frac{sin ( x )}{x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (cos (x) ln (x) + \frac{sin ( x )}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 3 (\frac{d}{d x} (cos (x) ln (x)) + \frac{d}{d x} (\frac{sin ( x )}{x}))

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

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

= 3 (- sin (x) ln (x) + \frac{cos ( x )}{x} + \frac{x cos ( x ) - sin ( x )}{x ^{2}})

Simplify

3 (- sin (x) ln (x) + \frac{cos ( x )}{x} + \frac{x cos ( x ) - sin ( x )}{x ^{2}}) : \frac{3 ( 2 x cos ( x ) - sin ( x ) - x ^{2} sin ( x ) ln ( x ) )}{x ^{2}}

= \frac{3 ( 2 x cos ( x ) - sin ( x ) - x ^{2} sin ( x ) ln ( x ) )}{x ^{2}}

\frac{d}{d x} (ln (4 + x^{2}))

\int 16 tan^{3} (x) sec (x) d x

x \to - 1 lim (\frac{x ^{4} - 1}{x + 1})

x \to 0 - lim ((1 - \frac{1}{x})^{x})

\frac{d}{d x} (x^{3} ln (7 x))

What is the derivative of 3(cos(x)ln(x)+(sin(x))/x) ?
The derivative of 3(cos(x)ln(x)+(sin(x))/x) is (3(2xcos(x)-sin(x)-x^2sin(x)ln(x)))/(x^2)
What is the first derivative of 3(cos(x)ln(x)+(sin(x))/x) ?
The first derivative of 3(cos(x)ln(x)+(sin(x))/x) is (3(2xcos(x)-sin(x)-x^2sin(x)ln(x)))/(x^2)