What is the derivative of \sqrt[3]{cos(2x+ln(3x)}) ?

The derivative of \sqrt[3]{cos(2x+ln(3x)}) is (-2xsin(2x)+1)/(3x(cos(2x)+ln(3x))^{2/3)}

What is the first derivative of \sqrt[3]{cos(2x+ln(3x)}) ?

The first derivative of \sqrt[3]{cos(2x+ln(3x)}) is (-2xsin(2x)+1)/(3x(cos(2x)+ln(3x))^{2/3)}

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\frac{d}{d x} (3 cos (2 x) + ln (3 x))

\frac{- 2 x sin ( 2 x ) + 1}{3 x ( cos ( 2 x ) + ln ( 3 x ) ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 cos (2 x) + ln (3 x))

Apply the chain rule:

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

= \frac{1}{3 ( cos ( 2 x ) + ln ( 3 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (cos (2 x) + ln (3 x))

\frac{d}{d x} (cos (2 x) + ln (3 x)) = - sin (2 x) \cdot 2 + \frac{1}{x}

= \frac{1}{3 ( cos ( 2 x ) + ln ( 3 x ) ) ^{\frac{2}{3}}} (- sin (2 x) \cdot 2 + \frac{1}{x})

Simplify

\frac{1}{3 ( cos ( 2 x ) + ln ( 3 x ) ) ^{\frac{2}{3}}} (- sin (2 x) \cdot 2 + \frac{1}{x}) : \frac{- 2 x sin ( 2 x ) + 1}{3 x ( cos ( 2 x ) + ln ( 3 x ) ) ^{\frac{2}{3}}}

= \frac{- 2 x sin ( 2 x ) + 1}{3 x ( cos ( 2 x ) + ln ( 3 x ) ) ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{1 + csc ( x ^{8} )}{1 - cot ( x ^{8} )})

y^{^{'}} - y sin (x) = 2 sin (x)

\frac{\partial}{\partial x} (sin (z^{3}) cos (x y))

\int \frac{x}{( x ^{2} + 4 x + 5 ) ^{2}} d x

x^{^{''}} + 3 x^{^{'}} + 4 x = 0

What is the derivative of \sqrt[3]{cos(2x+ln(3x)}) ?
The derivative of \sqrt[3]{cos(2x+ln(3x)}) is (-2xsin(2x)+1)/(3x(cos(2x)+ln(3x))^{2/3)}
What is the first derivative of \sqrt[3]{cos(2x+ln(3x)}) ?
The first derivative of \sqrt[3]{cos(2x+ln(3x)}) is (-2xsin(2x)+1)/(3x(cos(2x)+ln(3x))^{2/3)}