What is the derivative of \sqrt[3]{6x^4+7x^3} ?

The derivative of \sqrt[3]{6x^4+7x^3} is (x^2(8x+7))/((x^3)^{2/3)(6x+7)^{2/3}}

What is the first derivative of \sqrt[3]{6x^4+7x^3} ?

The first derivative of \sqrt[3]{6x^4+7x^3} is (x^2(8x+7))/((x^3)^{2/3)(6x+7)^{2/3}}

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derivative of

3 6 x^{4} + 7 x^{3}

\frac{x ^{2} ( 8 x + 7 )}{( x ^{3} ) ^{\frac{2}{3}} ( 6 x + 7 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 6 x^{4} + 7 x^{3})

Apply the chain rule:

\frac{1}{3 ( 6 x ^{4} + 7 x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x^{4} + 7 x^{3})

= \frac{1}{3 ( 6 x ^{4} + 7 x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x^{4} + 7 x^{3})

\frac{d}{d x} (6 x^{4} + 7 x^{3}) = 24 x^{3} + 21 x^{2}

= \frac{1}{3 ( 6 x ^{4} + 7 x ^{3} ) ^{\frac{2}{3}}} (24 x^{3} + 21 x^{2})

Simplify

\frac{1}{3 ( 6 x ^{4} + 7 x ^{3} ) ^{\frac{2}{3}}} (24 x^{3} + 21 x^{2}) : \frac{x ^{2} ( 8 x + 7 )}{( x ^{3} ) ^{\frac{2}{3}} ( 6 x + 7 ) ^{\frac{2}{3}}}

= \frac{x ^{2} ( 8 x + 7 )}{( x ^{3} ) ^{\frac{2}{3}} ( 6 x + 7 ) ^{\frac{2}{3}}}

\frac{d}{d x} ((6 x + 4) (3 x^{2} + 2))

x \to - \infty lim (\frac{5 x ^{4} + e ^{5 x}}{x ^{4}})

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

(4 x + 4 y)^{3} = 64 x^{3} + 64 y^{3}

g (t) = \frac{7}{t}

What is the derivative of \sqrt[3]{6x^4+7x^3} ?
The derivative of \sqrt[3]{6x^4+7x^3} is (x^2(8x+7))/((x^3)^{2/3)(6x+7)^{2/3}}
What is the first derivative of \sqrt[3]{6x^4+7x^3} ?
The first derivative of \sqrt[3]{6x^4+7x^3} is (x^2(8x+7))/((x^3)^{2/3)(6x+7)^{2/3}}