What is the derivative of-5x^{1/3} ?

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

What is the first derivative of-5x^{1/3} ?

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

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

- \frac{5}{3 x ^{\frac{2}{3}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 5 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

- 5 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : - \frac{5}{3 x ^{\frac{2}{3}}}

= - \frac{5}{3 x ^{\frac{2}{3}}}

\frac{d}{d t} (e^{t} (sin (t) + cos (t)))

y^{^{'''}} + 5 y^{^{''}} - 8 y^{^{'}} - 48 y = 0

\int e - x cos (2 x) d x

\int \frac{e ^{a x + b} - e ^{b x + a}}{e ^{a x}} d x

- 9 y^{^{''}} + 81 y = 0

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