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Popular Calculus >

derivative of 8x-5/(\sqrt[3]{x^2}+e)

Solution

\frac{d}{d x} (8 x - \frac{5}{3 x ^{2}} + e)

Solution

\frac{10}{3 x ^{\frac{5}{3}}} + 8

Solution steps

\frac{d}{d x} (8 x - \frac{5}{3 x ^{2}} + e)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (8 x) - \frac{d}{d x} (\frac{5}{3 x ^{2}}) + \frac{d e}{d x}

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (\frac{5}{3 x ^{2}}) = - \frac{10}{3 x ^{\frac{5}{3}}}

\frac{d e}{d x} = 0

= 8 - (- \frac{10}{3 x ^{\frac{5}{3}}}) + 0

Simplify

= \frac{10}{3 x ^{\frac{5}{3}}} + 8

Graph

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(1 + ln (x) + \frac{y}{x}) d x = (8 - ln (x)) d y

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Frequently Asked Questions (FAQ)

What is the derivative of 8x-5/(\sqrt[3]{x^2}+e) ?
The derivative of 8x-5/(\sqrt[3]{x^2}+e) is (10)/(3x^{5/3)}+8
What is the first derivative of 8x-5/(\sqrt[3]{x^2}+e) ?
The first derivative of 8x-5/(\sqrt[3]{x^2}+e) is (10)/(3x^{5/3)}+8