What is the derivative of (1+x^4^{2/3}) ?

The derivative of (1+x^4^{2/3}) is (8x^3)/(3(1+x^4)^{1/3)}

What is the first derivative of (1+x^4^{2/3}) ?

The first derivative of (1+x^4^{2/3}) is (8x^3)/(3(1+x^4)^{1/3)}

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\frac{d}{d x} ((1 + x^{4})^{\frac{2}{3}})

\frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((1 + x^{4})^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}} \frac{d}{d x} (1 + x^{4})

= \frac{2}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}} \frac{d}{d x} (1 + x^{4})

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

= \frac{2}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}} \cdot 4 x^{3}

Simplify

\frac{2}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}} \cdot 4 x^{3} : \frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

= \frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

(4) (8.6)

f (x) = (4 x + 1)

\frac{\partial}{\partial x} (ln (3 x + 5 y))

\frac{d}{d x} ((2 x)^{2})

f (x) = e^{2 x}

What is the derivative of (1+x^4^{2/3}) ?
The derivative of (1+x^4^{2/3}) is (8x^3)/(3(1+x^4)^{1/3)}
What is the first derivative of (1+x^4^{2/3}) ?
The first derivative of (1+x^4^{2/3}) is (8x^3)/(3(1+x^4)^{1/3)}