What is the derivative of f(x)=(x^7+5x)^{1/3} ?

The derivative of f(x)=(x^7+5x)^{1/3} is (7x^6+5)/(3(x^7+5x)^{2/3)}

What is the first derivative of f(x)=(x^7+5x)^{1/3} ?

The first derivative of f(x)=(x^7+5x)^{1/3} is (7x^6+5)/(3(x^7+5x)^{2/3)}

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derivative of

f (x) = (x^{7} + 5 x)^{\frac{1}{3}}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of f(x)=(x^7+5x)^{1/3} ?
The derivative of f(x)=(x^7+5x)^{1/3} is (7x^6+5)/(3(x^7+5x)^{2/3)}
What is the first derivative of f(x)=(x^7+5x)^{1/3} ?
The first derivative of f(x)=(x^7+5x)^{1/3} is (7x^6+5)/(3(x^7+5x)^{2/3)}