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

The derivative of \sqrt[3]{5x^3-pix+1} is (15x^2-pi)/(3(5x^3-pix+1)^{2/3)}

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

The first derivative of \sqrt[3]{5x^3-pix+1} is (15x^2-pi)/(3(5x^3-pix+1)^{2/3)}

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\frac{15 x ^{2} - π}{3 ( 5 x ^{3} - π x + 1 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{3} - π x + 1) = 15 x^{2} - π

= \frac{1}{3 ( 5 x ^{3} - π x + 1 ) ^{\frac{2}{3}}} (15 x^{2} - π)

Simplify

\frac{1}{3 ( 5 x ^{3} - π x + 1 ) ^{\frac{2}{3}}} (15 x^{2} - π) : \frac{15 x ^{2} - π}{3 ( 5 x ^{3} - π x + 1 ) ^{\frac{2}{3}}}

= \frac{15 x ^{2} - π}{3 ( 5 x ^{3} - π x + 1 ) ^{\frac{2}{3}}}

y^{^{''}} - 14 y^{^{'}} + 48 y = 0

\frac{3}{s \cdot ( s + 2 )}

8 x^{2} - 5 x, x^{3} - 8 x + 3

\int x + 10 d x

(e^{x} cos (x))^{^{'}}

What is the derivative of \sqrt[3]{5x^3-pix+1} ?
The derivative of \sqrt[3]{5x^3-pix+1} is (15x^2-pi)/(3(5x^3-pix+1)^{2/3)}
What is the first derivative of \sqrt[3]{5x^3-pix+1} ?
The first derivative of \sqrt[3]{5x^3-pix+1} is (15x^2-pi)/(3(5x^3-pix+1)^{2/3)}