What is the derivative of 4x^{-1/3}+9/(x^{5/3}) ?

The derivative of 4x^{-1/3}+9/(x^{5/3}) is -4/(3x^{4/3)}-(15)/(x^{8/3)}

What is the first derivative of 4x^{-1/3}+9/(x^{5/3}) ?

The first derivative of 4x^{-1/3}+9/(x^{5/3}) is -4/(3x^{4/3)}-(15)/(x^{8/3)}

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\frac{d}{d x} (4 x^{- \frac{1}{3}} + \frac{9}{x ^{\frac{5}{3}}})

- \frac{4}{3 x ^{\frac{4}{3}}} - \frac{15}{x ^{\frac{8}{3}}}

Solution steps

\frac{d}{d x} (4 x^{- \frac{1}{3}} + \frac{9}{x ^{\frac{5}{3}}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{- \frac{1}{3}}) + \frac{d}{d x} (\frac{9}{x ^{\frac{5}{3}}})

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

\frac{d}{d x} (\frac{9}{x ^{\frac{5}{3}}}) = - \frac{15}{x ^{\frac{8}{3}}}

= - \frac{4}{3 x ^{\frac{4}{3}}} - \frac{15}{x ^{\frac{8}{3}}}

\frac{d y}{d x}, x cos (2 x + 3 y) = y sin (x)

\int 2 t - t - \frac{9}{t ^{2}} d t

x \to 0 lim (x^{2} - 4)

\int \frac{x ^{2}}{( 1 - y ^{2} )}

e^{a x}

What is the derivative of 4x^{-1/3}+9/(x^{5/3}) ?
The derivative of 4x^{-1/3}+9/(x^{5/3}) is -4/(3x^{4/3)}-(15)/(x^{8/3)}
What is the first derivative of 4x^{-1/3}+9/(x^{5/3}) ?
The first derivative of 4x^{-1/3}+9/(x^{5/3}) is -4/(3x^{4/3)}-(15)/(x^{8/3)}