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Popular >

derivative of 5ln(cos(x))

Solution

\frac{d}{d x} (5 ln (cos (x)))

Solution

- 5 tan (x)

Solution steps

\frac{d}{d x} (5 ln (cos (x)))

Take the constant out:

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

= 5 \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)

= 5 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

5 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 5 tan (x)

= - 5 tan (x)

Graph

Popular Examples

limit as x approaches 0+of 1/(6x)

x \to 0 + lim (\frac{1}{6 x})

limit as x approaches 0 of 2((a^x-1)/x)

x \to 0 lim (2 (\frac{a ^{x} - 1}{x}))

integral from 1 to 12 of 1/(x-10)

\int_{1}^{12} \frac{1}{x - 10} d x

(\partial)/(\partial x)((e^x)/(x^2+10))

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

sum from n=0 to infinity of (2n+1)/(n!)

n = 0 \sum \infty \frac{2 n + 1}{n !}

Frequently Asked Questions (FAQ)

What is the derivative of 5ln(cos(x)) ?
The derivative of 5ln(cos(x)) is -5tan(x)
What is the first derivative of 5ln(cos(x)) ?
The first derivative of 5ln(cos(x)) is -5tan(x)