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Popular >

derivative of-ln|cos(x|)

Solution

\frac{d}{d x} (- ln ∣ cos (x) ∣)

Solution

tan (x)

Solution steps

\frac{d}{d x} (- ln ∣ cos (x) ∣)

Take the constant out:

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

= - \frac{d}{d x} (ln ∣ cos (x) ∣)

Apply the chain rule:

\frac{1}{∣ cos ( x ) ∣} \frac{d}{d x} (∣ cos (x) ∣)

= \frac{1}{∣ cos ( x ) ∣} \frac{d}{d x} (∣ cos (x) ∣)

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

= - \frac{1}{∣ cos ( x ) ∣} (- \frac{cos ( x ) sin ( x )}{∣ cos ( x ) ∣})

Simplify

- \frac{1}{∣ cos ( x ) ∣} (- \frac{cos ( x ) sin ( x )}{∣ cos ( x ) ∣}) : tan (x)

= tan (x)

Popular Examples

derivative of f(x)=(-3x^2-3)^4 derivative of

f (x) = (- 3 x^{2} - 3)^{4}

limit as t approaches 0 of cos(3t)

t \to 0 lim (cos (3 t))

(\partial)/(\partial z)(((x+y))/((y+z)))

\frac{\partial}{\partial z} (\frac{( x + y )}{( y + z )})

integral of (e^θ)/(a+be^θ)

\int \frac{e ^{θ}}{a + b e ^{θ}} d θ

integral of 4-3(1+x^2)^{-1}

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

Frequently Asked Questions (FAQ)

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