What is the derivative of 4ln(cos(x)) ?

The derivative of 4ln(cos(x)) is -4tan(x)

What is the first derivative of 4ln(cos(x)) ?

The first derivative of 4ln(cos(x)) is -4tan(x)

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\frac{d}{d x} (4 ln (cos (x)))

- 4 tan (x)

Solution steps

\frac{d}{d x} (4 ln (cos (x)))

Take the constant out:

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

= 4 \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)

= 4 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

4 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 4 tan (x)

= - 4 tan (x)

x \to 3 - lim (2 x - 1)

\int_{1}^{4} 5 t ln (t) d t

x \to - 3 lim (- \frac{5}{( x + 3 ) ^{2}})

\frac{d}{d x} (\frac{8 - x e ^{x}}{x + e ^{x}})

4 y^{^{'}} = \frac{4 x y + 8 x ^{2} + 2 y ^{2}}{x ^{2}}

What is the derivative of 4ln(cos(x)) ?
The derivative of 4ln(cos(x)) is -4tan(x)
What is the first derivative of 4ln(cos(x)) ?
The first derivative of 4ln(cos(x)) is -4tan(x)