What is the derivative of (cos(x)(ln(tan(x)))) ?

The derivative of (cos(x)(ln(tan(x)))) is -sin(x)ln(tan(x))+2csc(2x)cos(x)

What is the first derivative of (cos(x)(ln(tan(x)))) ?

The first derivative of (cos(x)(ln(tan(x)))) is -sin(x)ln(tan(x))+2csc(2x)cos(x)

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

- sin (x) ln (tan (x)) + 2 csc (2 x) cos (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (tan (x))) = 2 csc (2 x)

= (- sin (x)) ln (tan (x)) + 2 csc (2 x) cos (x)

Simplify

= - sin (x) ln (tan (x)) + 2 csc (2 x) cos (x)

(2 x + 3)^{\frac{1}{4}}

y^{2} + 8 x = 16, y^{2} - 24 x = 48

(8 x)^{2 x}

\frac{\partial}{\partial s} (\frac{s - 2 r}{t})

\int \frac{3 x + 1}{x} d x

What is the derivative of (cos(x)(ln(tan(x)))) ?
The derivative of (cos(x)(ln(tan(x)))) is -sin(x)ln(tan(x))+2csc(2x)cos(x)
What is the first derivative of (cos(x)(ln(tan(x)))) ?
The first derivative of (cos(x)(ln(tan(x)))) is -sin(x)ln(tan(x))+2csc(2x)cos(x)