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Popular >

derivative of-ln(sin(t))

Solution

derivative of

- ln (sin (t))

Solution

- cot (t)

Solution steps

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

Take the constant out:

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

= - \frac{d}{d t} (ln (sin (t)))

Apply the chain rule:

\frac{1}{sin ( t )} \frac{d}{d t} (sin (t))

= \frac{1}{sin ( t )} \frac{d}{d t} (sin (t))

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

= - \frac{1}{sin ( t )} cos (t)

Simplify

- \frac{1}{sin ( t )} cos (t) : - cot (t)

= - cot (t)

Popular Examples

integral of (x+5)/((x^2+5)^3)

\int \frac{x + 5}{( x ^{2} + 5 ) ^{3}} d x

(\partial)/(\partial x)(x^6y-3x^5y^2)

\frac{\partial}{\partial x} (x^{6} y - 3 x^{5} y^{2})

(\partial)/(\partial x)(x(3-2x-y))

\frac{\partial}{\partial x} (x (3 - 2 x - y))

derivative of \sqrt[4]{1-x^2}

integral of e^x+5

\int e^{x} + 5 d x

Frequently Asked Questions (FAQ)

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