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Popular >

derivative of ln(cos(5x))

Solution

derivative of

ln (cos (5 x))

Solution

- 5 tan (5 x)

Solution steps

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

Apply the chain rule:

\frac{1}{cos ( 5 x )} \frac{d}{d x} (cos (5 x))

= \frac{1}{cos ( 5 x )} \frac{d}{d x} (cos (5 x))

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

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

Simplify

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

= - 5 tan (5 x)

Popular Examples

y^{''}-5y^'+4y=0,y(0)=-5,y^'(0)=3

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = - 5, y^{^{'}} (0) = 3

limit as x approaches c of 9/8 (7/8)

x \to c lim (\frac{9}{8} (\frac{7}{8}))

integral of 1/(xsqrt(289x^2-289))

\int \frac{1}{x 289 x ^{2} - 289} d x

(\partial)/(\partial x)(-xy-x^4-y^4)

\frac{\partial}{\partial x} (- x y - x^{4} - y^{4})

(\partial)/(\partial x)((e^{x^2}+e^{y^2})^2)

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

Frequently Asked Questions (FAQ)

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