What is the derivative of f(x)=(7x^3+x^2)^{2/3} ?

The derivative of f(x)=(7x^3+x^2)^{2/3} is (2(21x^2+2x))/(3(7x^3+x^2)^{1/3)}

What is the first derivative of f(x)=(7x^3+x^2)^{2/3} ?

The first derivative of f(x)=(7x^3+x^2)^{2/3} is (2(21x^2+2x))/(3(7x^3+x^2)^{1/3)}

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derivative of

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

\frac{2 ( 21 x ^{2} + 2 x )}{3 ( 7 x ^{3} + x ^{2} ) ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

What is the derivative of f(x)=(7x^3+x^2)^{2/3} ?
The derivative of f(x)=(7x^3+x^2)^{2/3} is (2(21x^2+2x))/(3(7x^3+x^2)^{1/3)}
What is the first derivative of f(x)=(7x^3+x^2)^{2/3} ?
The first derivative of f(x)=(7x^3+x^2)^{2/3} is (2(21x^2+2x))/(3(7x^3+x^2)^{1/3)}