What is the derivative of cos(xln(cos(x))) ?

The derivative of cos(xln(cos(x))) is -sin(x)-ln(cos(x))sin(x)

What is the first derivative of cos(xln(cos(x))) ?

The first derivative of cos(xln(cos(x))) is -sin(x)-ln(cos(x))sin(x)

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

- sin (x) - ln (cos (x)) sin (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- sin (x)) ln (cos (x)) + (- tan (x)) cos (x) : - sin (x) - ln (cos (x)) sin (x)

= - sin (x) - ln (cos (x)) sin (x)

\frac{d y}{d t} = 2 y + 2 t^{2} - \frac{10}{3} t

\int 2 z d z

x^{5} sin (x)

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

\frac{d}{d x} (4 - x^{\frac{2}{3}})

What is the derivative of cos(xln(cos(x))) ?
The derivative of cos(xln(cos(x))) is -sin(x)-ln(cos(x))sin(x)
What is the first derivative of cos(xln(cos(x))) ?
The first derivative of cos(xln(cos(x))) is -sin(x)-ln(cos(x))sin(x)