What is the derivative of 2x^{-7\sqrt[3]{x}} ?

The derivative of 2x^{-7\sqrt[3]{x}} is 2x^{-7\sqrt[3]{x}}(-(7ln(x))/(3x^{2/3)}-7/(x^{2/3)})

What is the first derivative of 2x^{-7\sqrt[3]{x}} ?

The first derivative of 2x^{-7\sqrt[3]{x}} is 2x^{-7\sqrt[3]{x}}(-(7ln(x))/(3x^{2/3)}-7/(x^{2/3)})

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

2 x^{- 7 3 x} (- \frac{7 ln ( x )}{3 x ^{\frac{2}{3}}} - \frac{7}{x ^{\frac{2}{3}}})

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{- 7 3 x} = e^{(- 7 3 x) l n (x)}

= 2 \frac{d}{d x} (e^{(- 7 3 x) l n (x)})

Apply the chain rule:

e^{(- 7 3 x) l n (x)} \frac{d}{d x} ((- 7 3 x) ln (x))

= e^{(- 7 3 x) l n (x)} \frac{d}{d x} ((- 7 3 x) ln (x))

\frac{d}{d x} ((- 7 3 x) ln (x)) = - \frac{7 ln ( x )}{3 x ^{\frac{2}{3}}} - \frac{7}{x ^{\frac{2}{3}}}

= 2 e^{(- 7 3 x) l n (x)} (- \frac{7 ln ( x )}{3 x ^{\frac{2}{3}}} - \frac{7}{x ^{\frac{2}{3}}})

Simplify

2 e^{(- 7 3 x) l n (x)} (- \frac{7 ln ( x )}{3 x ^{\frac{2}{3}}} - \frac{7}{x ^{\frac{2}{3}}}) : 2 x^{- 7 3 x} (- \frac{7 ln ( x )}{3 x ^{\frac{2}{3}}} - \frac{7}{x ^{\frac{2}{3}}})

= 2 x^{- 7 3 x} (- \frac{7 ln ( x )}{3 x ^{\frac{2}{3}}} - \frac{7}{x ^{\frac{2}{3}}})

n = 1 \sum \infty n! 2^{n} n^{- n}

1 + 4 x^{2}

5 (t - 4)

\int \frac{x ^{2} + 2 + x}{3 2 + x} d x

x^{2} \cdot 2

What is the derivative of 2x^{-7\sqrt[3]{x}} ?
The derivative of 2x^{-7\sqrt[3]{x}} is 2x^{-7\sqrt[3]{x}}(-(7ln(x))/(3x^{2/3)}-7/(x^{2/3)})
What is the first derivative of 2x^{-7\sqrt[3]{x}} ?
The first derivative of 2x^{-7\sqrt[3]{x}} is 2x^{-7\sqrt[3]{x}}(-(7ln(x))/(3x^{2/3)}-7/(x^{2/3)})