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Popular >

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

Solution

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

Solution

- tan (x)

Solution steps

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

Simplify

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

= \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)

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

Simplify

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

= - tan (x)

Popular Examples

derivative of (1+2x/((3x-1)^2))

\frac{d}{d x} (\frac{1 + 2 x}{( 3 x - 1 ) ^{2}})

(y+4)(dy)/(dx)=2xy+4y

(y + 4) \frac{d y}{d x} = 2 x y + 4 y

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\int (cos (6 x) - csc^{2} (x)) d x

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

derivative of (4+sec(θ))sin(θ)derivative of

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Frequently Asked Questions (FAQ)

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