What is the derivative of-2ln(cos(x)) ?

The derivative of-2ln(cos(x)) is 2tan(x)

What is the first derivative of-2ln(cos(x)) ?

The first derivative of-2ln(cos(x)) is 2tan(x)

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\frac{d}{d x} (- 2 ln (cos (x)))

2 tan (x)

Solution steps

\frac{d}{d x} (- 2 ln (cos (x)))

Take the constant out:

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

= - 2 \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)) = - sin (x)

= - 2 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

- 2 \cdot \frac{1}{cos ( x )} (- sin (x)) : 2 tan (x)

= 2 tan (x)

\int x \cdot e^{2 x^{2}} d x

y = \frac{x}{x + 5}

\int_{1}^{2} - x^{2} + 3 x - 2 d x

2 x^{2} \frac{d y}{d x} + 2 x y = y^{3}

\int 36 - 9 x^{2} d x

What is the derivative of-2ln(cos(x)) ?
The derivative of-2ln(cos(x)) is 2tan(x)
What is the first derivative of-2ln(cos(x)) ?
The first derivative of-2ln(cos(x)) is 2tan(x)