What is the derivative of-ln(xcos(x)) ?

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

What is the first derivative of-ln(xcos(x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = cos (x)

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

= - (\frac{1}{x} cos (x) + (- sin (x)) ln (x))

Simplify

- (\frac{1}{x} cos (x) + (- sin (x)) ln (x)) : - \frac{cos ( x )}{x} + sin (x) ln (x)

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

\int (5 cos (3 x) - 4 sin (5 x)) d x

n = 5 \sum \infty \frac{5 ^{n}}{1 2 ^{n}}

5 sin (3 t)

x \to \infty lim (\frac{9}{x} - 1)

f (x) = \frac{6 x ^{5} + 4 x}{x ^{4} + 3}

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