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

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

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

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

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

- cos (ln (cos (x))) tan (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 13}{2 x + 4})

x \to 6 lim (\frac{6 + x}{x})

\int \frac{2 x ^{3} - 1}{x + x ^{4}} d x

f (x) = tan^{2} (x^{3})

\int ln (21 t) d t

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