What is the derivative of \sqrt[4]{x^3-x+3} ?

The derivative of \sqrt[4]{x^3-x+3} is (3x^2-1)/(4(x^3-x+3)^{3/4)}

What is the first derivative of \sqrt[4]{x^3-x+3} ?

The first derivative of \sqrt[4]{x^3-x+3} is (3x^2-1)/(4(x^3-x+3)^{3/4)}

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of \sqrt[4]{x^3-x+3} ?
The derivative of \sqrt[4]{x^3-x+3} is (3x^2-1)/(4(x^3-x+3)^{3/4)}
What is the first derivative of \sqrt[4]{x^3-x+3} ?
The first derivative of \sqrt[4]{x^3-x+3} is (3x^2-1)/(4(x^3-x+3)^{3/4)}