What is the derivative of f(x)= 6/(\sqrt[9]{x^7+5)} ?

The derivative of f(x)= 6/(\sqrt[9]{x^7+5)} is -(14x^6)/(3(x^7+5)^{10/9)}

What is the first derivative of f(x)= 6/(\sqrt[9]{x^7+5)} ?

The first derivative of f(x)= 6/(\sqrt[9]{x^7+5)} is -(14x^6)/(3(x^7+5)^{10/9)}

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derivative of

- \frac{14 x ^{6}}{3 ( x ^{7} + 5 ) ^{\frac{10}{9}}}

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 6 \frac{d}{d x} ((x^{7} + 5)^{- \frac{1}{9}})

Apply the chain rule:

- \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \frac{d}{d x} (x^{7} + 5)

= - \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \frac{d}{d x} (x^{7} + 5)

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

= 6 (- \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \cdot 7 x^{6})

Simplify

6 (- \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \cdot 7 x^{6}) : - \frac{14 x ^{6}}{3 ( x ^{7} + 5 ) ^{\frac{10}{9}}}

= - \frac{14 x ^{6}}{3 ( x ^{7} + 5 ) ^{\frac{10}{9}}}

\int (a x + b) d x

\frac{d}{d x} (ln (arctan (cos (x))))

\int cos (x π) d x

\int_{0}^{2 π} cos^{2} (t) d t

y = 2^{x} + x^{2} (- 1 - x)^{x}

What is the derivative of f(x)= 6/(\sqrt[9]{x^7+5)} ?
The derivative of f(x)= 6/(\sqrt[9]{x^7+5)} is -(14x^6)/(3(x^7+5)^{10/9)}
What is the first derivative of f(x)= 6/(\sqrt[9]{x^7+5)} ?
The first derivative of f(x)= 6/(\sqrt[9]{x^7+5)} is -(14x^6)/(3(x^7+5)^{10/9)}