What is the derivative of (3+cos^3(3x)^{-1/3}) ?

The derivative of (3+cos^3(3x)^{-1/3}) is (3cos^2(3x)sin(3x))/((3+cos^3(3x))^{4/3)}

What is the first derivative of (3+cos^3(3x)^{-1/3}) ?

The first derivative of (3+cos^3(3x)^{-1/3}) is (3cos^2(3x)sin(3x))/((3+cos^3(3x))^{4/3)}

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

\frac{3 cos ^{2} ( 3 x ) sin ( 3 x )}{( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}}

Solution steps

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

Apply the chain rule:

- \frac{1}{3 ( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}} \frac{d}{d x} (3 + cos^{3} (3 x))

= - \frac{1}{3 ( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}} \frac{d}{d x} (3 + cos^{3} (3 x))

\frac{d}{d x} (3 + cos^{3} (3 x)) = - 9 cos^{2} (3 x) sin (3 x)

= - \frac{1}{3 ( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}} (- 9 cos^{2} (3 x) sin (3 x))

Simplify

- \frac{1}{3 ( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}} (- 9 cos^{2} (3 x) sin (3 x)) : \frac{3 cos ^{2} ( 3 x ) sin ( 3 x )}{( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}}

= \frac{3 cos ^{2} ( 3 x ) sin ( 3 x )}{( 3 + cos ^{3} ( 3 x ) ) ^{\frac{4}{3}}}

x \to 3 lim (2 x^{2} + 6)

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{9}{2}}} d t

y^{^{'}} = 0.5 - t + 2 y

x \to - 7 - lim (\frac{x}{x + 7})

\frac{\frac{1}{2}}{s}

What is the derivative of (3+cos^3(3x)^{-1/3}) ?
The derivative of (3+cos^3(3x)^{-1/3}) is (3cos^2(3x)sin(3x))/((3+cos^3(3x))^{4/3)}
What is the first derivative of (3+cos^3(3x)^{-1/3}) ?
The first derivative of (3+cos^3(3x)^{-1/3}) is (3cos^2(3x)sin(3x))/((3+cos^3(3x))^{4/3)}