What is the derivative of 8ln(cos(x)) ?

The derivative of 8ln(cos(x)) is -8tan(x)

What is the first derivative of 8ln(cos(x)) ?

The first derivative of 8ln(cos(x)) is -8tan(x)

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\frac{d}{d x} (8 ln (cos (x)))

- 8 tan (x)

Solution steps

\frac{d}{d x} (8 ln (cos (x)))

Take the constant out:

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

= 8 \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)

= 8 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

8 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 8 tan (x)

= - 8 tan (x)

\int \frac{( 4 + 10 x )}{7 + 4 x + 5 x ^{2}} d x

y^{^{'}} + 3 y = e^{- 2 x}

\int_{- 3}^{4} ((y + 12) - (y^{2})) d y

y^{^{''}} + 7 y^{^{'}} + 6 y = 0

f (x) = 2 (x)^{3} ln (x)

What is the derivative of 8ln(cos(x)) ?
The derivative of 8ln(cos(x)) is -8tan(x)
What is the first derivative of 8ln(cos(x)) ?
The first derivative of 8ln(cos(x)) is -8tan(x)