What is the derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) ?

The derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) is (16x^3+15x^2)/(3(x^3)^{2/3)(4x+5)^{2/3}}

What is the first derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) ?

The first derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) is (16x^3+15x^2)/(3(x^3)^{2/3)(4x+5)^{2/3}}

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derivative of

\frac{16 x ^{3} + 15 x ^{2}}{3 ( x ^{3} ) ^{\frac{2}{3}} ( 4 x + 5 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 4 x ^{4} + 5 x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x^{4} + 5 x^{3})

= \frac{1}{3 ( 4 x ^{4} + 5 x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x^{4} + 5 x^{3})

\frac{d}{d x} (4 x^{4} + 5 x^{3}) = 16 x^{3} + 15 x^{2}

= \frac{1}{3 ( 4 x ^{4} + 5 x ^{3} ) ^{\frac{2}{3}}} (16 x^{3} + 15 x^{2})

Simplify

\frac{1}{3 ( 4 x ^{4} + 5 x ^{3} ) ^{\frac{2}{3}}} (16 x^{3} + 15 x^{2}) : \frac{16 x ^{3} + 15 x ^{2}}{3 ( x ^{3} ) ^{\frac{2}{3}} ( 4 x + 5 ) ^{\frac{2}{3}}}

= \frac{16 x ^{3} + 15 x ^{2}}{3 ( x ^{3} ) ^{\frac{2}{3}} ( 4 x + 5 ) ^{\frac{2}{3}}}

What is the derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) ?
The derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) is (16x^3+15x^2)/(3(x^3)^{2/3)(4x+5)^{2/3}}
What is the first derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) ?
The first derivative of f(x)=(\sqrt[3]{4x^4+5x^3}) is (16x^3+15x^2)/(3(x^3)^{2/3)(4x+5)^{2/3}}