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Popular >

derivative of log_{e}(cos(4x))

Solution

\frac{d}{d x} (lo g_{e} (cos (4 x)))

Solution

- 4 tan (4 x)

Solution steps

\frac{d}{d x} (lo g_{e} (cos (4 x)))

Simplify

lo g_{e} (cos (4 x)) : ln (cos (4 x))

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

Apply the chain rule:

\frac{1}{cos ( 4 x )} \frac{d}{d x} (cos (4 x))

= \frac{1}{cos ( 4 x )} \frac{d}{d x} (cos (4 x))

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

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

Simplify

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

= - 4 tan (4 x)

Popular Examples

integral of xln(x^5)

\int x ln (x^{5}) d x

integral from 0 to pi/4 of xsin(2x)

\int_{0}^{\frac{π}{4}} x sin (2 x) d x

integral from 0 to 9 of (sqrt(x)-1/3 x)

\int_{0}^{9} (x - \frac{1}{3} x) d x

integral of e^{2x}cos(7x)

\int e^{2 x} cos (7 x) d x

limit as z approaches 1-i of x+i(2x+y)

z \to 1 - i lim (x + i (2 x + y))

Frequently Asked Questions (FAQ)

What is the derivative of log_{e}(cos(4x)) ?
The derivative of log_{e}(cos(4x)) is -4tan(4x)
What is the first derivative of log_{e}(cos(4x)) ?
The first derivative of log_{e}(cos(4x)) is -4tan(4x)