What is the derivative of 2\sqrt[5]{(x^3+1^2}) ?

The derivative of 2\sqrt[5]{(x^3+1^2}) is (12x^2)/(5(x^3+1)^{3/5)}

What is the first derivative of 2\sqrt[5]{(x^3+1^2}) ?

The first derivative of 2\sqrt[5]{(x^3+1^2}) is (12x^2)/(5(x^3+1)^{3/5)}

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\frac{12 x ^{2}}{5 ( x ^{3} + 1 ) ^{\frac{3}{5}}}

Solution steps

Take the constant out:

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

Apply the chain rule:

\frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} ((x^{3} + 1)^{2})

= \frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} ((x^{3} + 1)^{2})

\frac{d}{d x} ((x^{3} + 1)^{2}) = 6 x^{2} (x^{3} + 1)

= 2 \cdot \frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \cdot 6 x^{2} (x^{3} + 1)

Simplify

2 \cdot \frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \cdot 6 x^{2} (x^{3} + 1) : \frac{12 x ^{2}}{5 ( x ^{3} + 1 ) ^{\frac{3}{5}}}

= \frac{12 x ^{2}}{5 ( x ^{3} + 1 ) ^{\frac{3}{5}}}

\frac{\partial}{\partial x} (x^{0.5})

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\frac{\partial}{\partial t} (e^{t} cos (t))

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What is the derivative of 2\sqrt[5]{(x^3+1^2}) ?
The derivative of 2\sqrt[5]{(x^3+1^2}) is (12x^2)/(5(x^3+1)^{3/5)}
What is the first derivative of 2\sqrt[5]{(x^3+1^2}) ?
The first derivative of 2\sqrt[5]{(x^3+1^2}) is (12x^2)/(5(x^3+1)^{3/5)}