What is the derivative of 25^{1/3}x^{2/3} ?

The derivative of 25^{1/3}x^{2/3} is (2*25^{1/3})/(3x^{1/3)}

What is the first derivative of 25^{1/3}x^{2/3} ?

The first derivative of 25^{1/3}x^{2/3} is (2*25^{1/3})/(3x^{1/3)}

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derivative of

2 5^{\frac{1}{3}} x^{\frac{2}{3}}

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

Solution steps

\frac{d}{d x} (2 5^{\frac{1}{3}} x^{\frac{2}{3}})

Take the constant out:

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

= 2 5^{\frac{1}{3}} \frac{d}{d x} (x^{\frac{2}{3}})

Apply the Power Rule:

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

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

Simplify

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

= \frac{2 \cdot 2 5 ^{\frac{1}{3}}}{3 x ^{\frac{1}{3}}}

f (x) = tan (x) + 5

\int_{0}^{10} 3 x^{2} - 42 x + 135 d x

\frac{d y}{d x}, y^{2} = x - y

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

\int tan (u) d u

What is the derivative of 25^{1/3}x^{2/3} ?
The derivative of 25^{1/3}x^{2/3} is (2*25^{1/3})/(3x^{1/3)}
What is the first derivative of 25^{1/3}x^{2/3} ?
The first derivative of 25^{1/3}x^{2/3} is (2*25^{1/3})/(3x^{1/3)}