What is the derivative of \sqrt[3]{7x^4+8x^3} ?

The derivative of \sqrt[3]{7x^4+8x^3} is (28x^3+24x^2)/(3(x^3)^{2/3)(7x+8)^{2/3}}

What is the first derivative of \sqrt[3]{7x^4+8x^3} ?

The first derivative of \sqrt[3]{7x^4+8x^3} is (28x^3+24x^2)/(3(x^3)^{2/3)(7x+8)^{2/3}}

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derivative of

3 7 x^{4} + 8 x^{3}

\frac{28 x ^{3} + 24 x ^{2}}{3 ( x ^{3} ) ^{\frac{2}{3}} ( 7 x + 8 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 7 x^{4} + 8 x^{3})

Apply the chain rule:

\frac{1}{3 ( 7 x ^{4} + 8 x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (7 x^{4} + 8 x^{3})

= \frac{1}{3 ( 7 x ^{4} + 8 x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (7 x^{4} + 8 x^{3})

\frac{d}{d x} (7 x^{4} + 8 x^{3}) = 28 x^{3} + 24 x^{2}

= \frac{1}{3 ( 7 x ^{4} + 8 x ^{3} ) ^{\frac{2}{3}}} (28 x^{3} + 24 x^{2})

Simplify

\frac{1}{3 ( 7 x ^{4} + 8 x ^{3} ) ^{\frac{2}{3}}} (28 x^{3} + 24 x^{2}) : \frac{28 x ^{3} + 24 x ^{2}}{3 ( x ^{3} ) ^{\frac{2}{3}} ( 7 x + 8 ) ^{\frac{2}{3}}}

= \frac{28 x ^{3} + 24 x ^{2}}{3 ( x ^{3} ) ^{\frac{2}{3}} ( 7 x + 8 ) ^{\frac{2}{3}}}

\frac{200}{0.9 + 0.1 e ^{2 h}}

\int \frac{\frac{1}{z} - x ^{2}}{x ^{2}} d x

\int (sec^{2} (θ) - sin (θ)) d θ

\int - 3 t^{2} cos (t) d t

n = 1 \sum \infty \frac{- 3}{2 ^{n}}

What is the derivative of \sqrt[3]{7x^4+8x^3} ?
The derivative of \sqrt[3]{7x^4+8x^3} is (28x^3+24x^2)/(3(x^3)^{2/3)(7x+8)^{2/3}}
What is the first derivative of \sqrt[3]{7x^4+8x^3} ?
The first derivative of \sqrt[3]{7x^4+8x^3} is (28x^3+24x^2)/(3(x^3)^{2/3)(7x+8)^{2/3}}