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

The derivative of f(x)=3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}

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

The first derivative of f(x)=3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}

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derivative of

f (x) = 3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}

\frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (5 x^{\frac{4}{3}}) = \frac{20 x ^{\frac{1}{3}}}{3}

= \frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3}

Simplify

\frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3} : \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

= \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

y = e^{x}, y = e^{4 x}, x = 1

\frac{1}{( ( s - 1 ) ^{2} + 4 )}

\frac{d}{d x} (\frac{1 - x}{x ^{2} + 1})

y^{^{''}} - 4 y + 4 y = 0

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

What is the derivative of f(x)=3x^{1/3}-5x^{4/3} ?
The derivative of f(x)=3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}
What is the first derivative of f(x)=3x^{1/3}-5x^{4/3} ?
The first derivative of f(x)=3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}