What is the derivative of cos(-5ln(-3x-1)) ?

The derivative of cos(-5ln(-3x-1)) is (15sin(5ln(-1-3x)))/(-1-3x)

What is the first derivative of cos(-5ln(-3x-1)) ?

The first derivative of cos(-5ln(-3x-1)) is (15sin(5ln(-1-3x)))/(-1-3x)

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\frac{d}{d x} (cos (- 5 ln (- 3 x - 1)))

\frac{15 sin ( 5 ln ( - 1 - 3 x ) )}{- 1 - 3 x}

Solution steps

\frac{d}{d x} (cos (- 5 ln (- 3 x - 1)))

Simplify

cos (- 5 ln (- 3 x - 1)) : cos (5 ln (- 1 - 3 x))

= \frac{d}{d x} (cos (5 ln (- 1 - 3 x)))

Apply the chain rule:

- sin (5 ln (- 1 - 3 x)) \frac{d}{d x} (5 ln (- 1 - 3 x))

= - sin (5 ln (- 1 - 3 x)) \frac{d}{d x} (5 ln (- 1 - 3 x))

\frac{d}{d x} (5 ln (- 1 - 3 x)) = - \frac{15}{- 1 - 3 x}

= - sin (5 ln (- 1 - 3 x)) (- \frac{15}{- 1 - 3 x})

Simplify

- sin (5 ln (- 1 - 3 x)) (- \frac{15}{- 1 - 3 x}) : \frac{15 sin ( 5 ln ( - 1 - 3 x ) )}{- 1 - 3 x}

= \frac{15 sin ( 5 ln ( - 1 - 3 x ) )}{- 1 - 3 x}

\int \frac{( 1 + y )}{y} d y

f (x) = (x + 1)

\int_{0}^{l n (2)} e^{x} - 1 d x

y = (6 x + 5)^{2}

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

What is the derivative of cos(-5ln(-3x-1)) ?
The derivative of cos(-5ln(-3x-1)) is (15sin(5ln(-1-3x)))/(-1-3x)
What is the first derivative of cos(-5ln(-3x-1)) ?
The first derivative of cos(-5ln(-3x-1)) is (15sin(5ln(-1-3x)))/(-1-3x)