What is the derivative of \sqrt[4]{1+2x+x^3} ?

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - 2 lim (3 x^{2} - 5 x + 7)

(- 3, 5), (6, - 1)

\int (3 - 2 x) e^{- x} d x

\int sec (7 x) tan (7 x) d x

\int y \cdot sin (y^{2}) d y

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