What is the derivative of 1/(\sqrt[5]{x^5-x^3+3}) ?

The derivative of 1/(\sqrt[5]{x^5-x^3+3}) is -(5x^4-3x^2)/(5(x^5-x^3+3)^{6/5)}

What is the first derivative of 1/(\sqrt[5]{x^5-x^3+3}) ?

The first derivative of 1/(\sqrt[5]{x^5-x^3+3}) is -(5x^4-3x^2)/(5(x^5-x^3+3)^{6/5)}

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- \frac{5 x ^{4} - 3 x ^{2}}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}}

Solution steps

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{5} - x^{3} + 3)

= - \frac{1}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{5} - x^{3} + 3)

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

= - \frac{1}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}} (5 x^{4} - 3 x^{2})

Simplify

- \frac{1}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}} (5 x^{4} - 3 x^{2}) : - \frac{5 x ^{4} - 3 x ^{2}}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}}

= - \frac{5 x ^{4} - 3 x ^{2}}{5 ( x ^{5} - x ^{3} + 3 ) ^{\frac{6}{5}}}

\frac{d}{d t} (- e^{t})

2 x^{3} + 3 x^{2} - 12 x + 8

\int_{0}^{\frac{π}{16}} tan (8 x) d x

\int_{- 4}^{4} 4 - ∣ x ∣ d x

\frac{\partial}{\partial y} (cos (x + e^{y}) e^{y})

What is the derivative of 1/(\sqrt[5]{x^5-x^3+3}) ?
The derivative of 1/(\sqrt[5]{x^5-x^3+3}) is -(5x^4-3x^2)/(5(x^5-x^3+3)^{6/5)}
What is the first derivative of 1/(\sqrt[5]{x^5-x^3+3}) ?
The first derivative of 1/(\sqrt[5]{x^5-x^3+3}) is -(5x^4-3x^2)/(5(x^5-x^3+3)^{6/5)}