What is the derivative of f(x)=-7x^{4/3}+4/(x^3) ?

The derivative of f(x)=-7x^{4/3}+4/(x^3) is (-28x^{13/3}-36)/(3x^4)

What is the first derivative of f(x)=-7x^{4/3}+4/(x^3) ?

The first derivative of f(x)=-7x^{4/3}+4/(x^3) is (-28x^{13/3}-36)/(3x^4)

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derivative of

f (x) = - 7 x^{\frac{4}{3}} + \frac{4}{x ^{3}}

\frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

Solution steps

\frac{d}{d x} (- 7 x^{\frac{4}{3}} + \frac{4}{x ^{3}})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (7 x^{\frac{4}{3}}) + \frac{d}{d x} (\frac{4}{x ^{3}})

\frac{d}{d x} (7 x^{\frac{4}{3}}) = \frac{28 x ^{\frac{1}{3}}}{3}

\frac{d}{d x} (\frac{4}{x ^{3}}) = - \frac{12}{x ^{4}}

= - \frac{28 x ^{\frac{1}{3}}}{3} - \frac{12}{x ^{4}}

Simplify

- \frac{28 x ^{\frac{1}{3}}}{3} - \frac{12}{x ^{4}} : \frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

= \frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

y^{2} = 4 x

y = 3 x - 5

(0, - 3), (1, - 2)

(- 1, 3)

x = 5

What is the derivative of f(x)=-7x^{4/3}+4/(x^3) ?
The derivative of f(x)=-7x^{4/3}+4/(x^3) is (-28x^{13/3}-36)/(3x^4)
What is the first derivative of f(x)=-7x^{4/3}+4/(x^3) ?
The first derivative of f(x)=-7x^{4/3}+4/(x^3) is (-28x^{13/3}-36)/(3x^4)