What is the derivative of \sqrt[3]{5x^7+6x^6} ?

The derivative of \sqrt[3]{5x^7+6x^6} is (35x^6+36x^5)/(3(x^6)^{2/3)(5x+6)^{2/3}}

What is the first derivative of \sqrt[3]{5x^7+6x^6} ?

The first derivative of \sqrt[3]{5x^7+6x^6} is (35x^6+36x^5)/(3(x^6)^{2/3)(5x+6)^{2/3}}

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derivative of

\frac{35 x ^{6} + 36 x ^{5}}{3 ( x ^{6} ) ^{\frac{2}{3}} ( 5 x + 6 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 5 x ^{7} + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 x^{7} + 6 x^{6})

= \frac{1}{3 ( 5 x ^{7} + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 x^{7} + 6 x^{6})

\frac{d}{d x} (5 x^{7} + 6 x^{6}) = 35 x^{6} + 36 x^{5}

= \frac{1}{3 ( 5 x ^{7} + 6 x ^{6} ) ^{\frac{2}{3}}} (35 x^{6} + 36 x^{5})

Simplify

\frac{1}{3 ( 5 x ^{7} + 6 x ^{6} ) ^{\frac{2}{3}}} (35 x^{6} + 36 x^{5}) : \frac{35 x ^{6} + 36 x ^{5}}{3 ( x ^{6} ) ^{\frac{2}{3}} ( 5 x + 6 ) ^{\frac{2}{3}}}

= \frac{35 x ^{6} + 36 x ^{5}}{3 ( x ^{6} ) ^{\frac{2}{3}} ( 5 x + 6 ) ^{\frac{2}{3}}}

\frac{5 d u}{d t} = u^{2}

cos (\frac{1}{x})

t \to 2 + lim (\frac{t + 2}{t ^{2} - 4})

6 sin (x)

\frac{1}{( 4 - x ^{2} )}

What is the derivative of \sqrt[3]{5x^7+6x^6} ?
The derivative of \sqrt[3]{5x^7+6x^6} is (35x^6+36x^5)/(3(x^6)^{2/3)(5x+6)^{2/3}}
What is the first derivative of \sqrt[3]{5x^7+6x^6} ?
The first derivative of \sqrt[3]{5x^7+6x^6} is (35x^6+36x^5)/(3(x^6)^{2/3)(5x+6)^{2/3}}