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

The derivative of \sqrt[5]{(3x^2+5x(1-x)^2}) is (12x^3-3x^2-14x+5)/(5((3x^2+5x)(1-x)^2)^{4/5)}

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

The first derivative of \sqrt[5]{(3x^2+5x(1-x)^2}) is (12x^3-3x^2-14x+5)/(5((3x^2+5x)(1-x)^2)^{4/5)}

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

\frac{12 x ^{3} - 3 x ^{2} - 14 x + 5}{5 ( ( 3 x ^{2} + 5 x ) ( 1 - x ) ^{2} ) ^{\frac{4}{5}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((3 x^{2} + 5 x) (1 - x)^{2}) = 12 x^{3} - 3 x^{2} - 14 x + 5

= \frac{1}{5 ( ( 3 x ^{2} + 5 x ) ( 1 - x ) ^{2} ) ^{\frac{4}{5}}} (12 x^{3} - 3 x^{2} - 14 x + 5)

Simplify

\frac{1}{5 ( ( 3 x ^{2} + 5 x ) ( 1 - x ) ^{2} ) ^{\frac{4}{5}}} (12 x^{3} - 3 x^{2} - 14 x + 5) : \frac{12 x ^{3} - 3 x ^{2} - 14 x + 5}{5 ( ( 3 x ^{2} + 5 x ) ( 1 - x ) ^{2} ) ^{\frac{4}{5}}}

= \frac{12 x ^{3} - 3 x ^{2} - 14 x + 5}{5 ( ( 3 x ^{2} + 5 x ) ( 1 - x ) ^{2} ) ^{\frac{4}{5}}}

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

\frac{d}{d x} (x^{5} e^{7 x})

x \to 1 lim ((x - 1)^{3 x - 3})

x \to 2 lim (x 13 - x^{2})

\frac{d}{d x} (x cos (x^{3}))

What is the derivative of \sqrt[5]{(3x^2+5x(1-x)^2}) ?
The derivative of \sqrt[5]{(3x^2+5x(1-x)^2}) is (12x^3-3x^2-14x+5)/(5((3x^2+5x)(1-x)^2)^{4/5)}
What is the first derivative of \sqrt[5]{(3x^2+5x(1-x)^2}) ?
The first derivative of \sqrt[5]{(3x^2+5x(1-x)^2}) is (12x^3-3x^2-14x+5)/(5((3x^2+5x)(1-x)^2)^{4/5)}