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

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

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

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

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

- 4 tan (x)

Solution steps

\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)) = - 4 cos^{3} (x) sin (x)

= \frac{1}{cos ^{4} ( x )} (- 4 cos^{3} (x) sin (x))

Simplify

\frac{1}{cos ^{4} ( x )} (- 4 cos^{3} (x) sin (x)) : - 4 tan (x)

= - 4 tan (x)

\int (5 y^{4}) d y

\int (2 x - 1) y^{2} sin (4 x y) d x

f (x) = 8 x - 3

f (x) = 2 e^{x} cos (x), at x = 0

\int 0.67 sin (100 π x + \frac{π}{3}) d x

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