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

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

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

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

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derivative of

sin (ln (cos (t)))

- cos (ln (cos (t))) tan (t)

Solution steps

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

Apply the chain rule:

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

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

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

= cos (ln (cos (t))) (- tan (t))

Simplify

= - cos (ln (cos (t))) tan (t)

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