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Popular >

derivative of 9ln(cos(x))

Solution

\frac{d}{d x} (9 ln (cos (x)))

Solution

- 9 tan (x)

Solution steps

\frac{d}{d x} (9 ln (cos (x)))

Take the constant out:

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

= 9 \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)

= 9 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

9 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 9 tan (x)

= - 9 tan (x)

Popular Examples

integral of sin^3(2x)sqrt(cos(2x))

\int sin^{3} (2 x) cos (2 x) d x

derivative of (4x^2-1/2 x(9x+8))

\frac{d}{d x} ((4 x^{2} - \frac{1}{2} x) (9 x + 8))

derivative of 3e^{4x}

\frac{d}{d x} (3 e^{4 x})

2 y^{^{'}} = 3 x y + 1

limit as x approaches 1 of (x^2-2x+1)cos(e^{1/(x-1)})

x \to 1 lim ((x^{2} - 2 x + 1) cos (e^{\frac{1}{x - 1}}))

Frequently Asked Questions (FAQ)

What is the derivative of 9ln(cos(x)) ?
The derivative of 9ln(cos(x)) is -9tan(x)
What is the first derivative of 9ln(cos(x)) ?
The first derivative of 9ln(cos(x)) is -9tan(x)