How do you find the derivative of ${(2 x^{2} - 5)}^{3} {(x^{3} + 6 x)}^{\frac{4}{3}}$ $(2x^2 -5)^3(x^3 +6x)^(4/3)$ ?

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How do you find the derivative of ${(2 x^{2} - 5)}^{3} {(x^{3} + 6 x)}^{\frac{4}{3}}$ $(2x^2 -5)^3(x^3 +6x)^(4/3)$ ?

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Answer 1 · 2018-05-24T16:43:52

$4 {(x^{3} + 6 x)}^{\frac{1}{3}} {(2 x^{2} - 5)}^{2} (5 x^{4} + 15 x^{2} - 10)$ $4(x^3+6x)^(1/3)(2x^2-5)^2(5x^4+15x^2-10)$

Explanation:

By the product and the chain rule we get
$3 {(2 x^{2} - 5)}^{2} \cdot 4 x {(x^{3} + 6 x)}^{\frac{4}{3}} + {(2 x^{2} - 5)}^{3} \cdot \frac{4}{3} {(x^{3} + 6 x)}^{\frac{1}{3}} (3 x^{2} + 6)$ $3(2x^2-5)^2*4x(x^3+6x)^(4/3)+(2x^2-5)^3*4/3(x^3+6x)^(1/3)(3x^2+6)$ which simplifies to my answer

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How do you find the derivative of ${(2 x^{2} - 5)}^{3} {(x^{3} + 6 x)}^{\frac{4}{3}}$ $(2x^2 -5)^3(x^3 +6x)^(4/3)$ ?

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Explanation:

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How do you find the derivative of (2x2−5)3(x3+6x)43(2x^2 -5)^3(x^3 +6x)^(4/3)?

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Explanation:

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How do you find the derivative of ${(2 x^{2} - 5)}^{3} {(x^{3} + 6 x)}^{\frac{4}{3}}$ $(2x^2 -5)^3(x^3 +6x)^(4/3)$ ?