Expert Answer to "Find the derivatives. y=ex3⋅(x6−3x)"

Dillard

Answered question

2021-05-31

Find the derivatives.

y = e^{\frac{x}{3}} \cdot (x^{6} - \frac{3}{x})

Ezra Herbert

Skilled2021-06-01Added 99 answers

The given function is

y = e^{\frac{x}{3}} \cdot (x^{6} - \frac{3}{x})

Obtain the derivative as follows.

\frac{d y}{d x} = \frac{d}{d x} [e^{\frac{x}{3}} (x^{6} - \frac{3}{x})]

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

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

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

Thus,

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

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