What is the derivative of (3/x ^{14}) ?

The derivative of (3/x ^{14}) is -(66961566)/(x^{15)}

What is the first derivative of (3/x ^{14}) ?

The first derivative of (3/x ^{14}) is -(66961566)/(x^{15)}

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\frac{d}{d x} ((\frac{3}{x})^{14})

- \frac{66961566}{x ^{15}}

Solution steps

\frac{d}{d x} ((\frac{3}{x})^{14})

Apply the chain rule:

14 (\frac{3}{x})^{13} \frac{d}{d x} (\frac{3}{x})

= 14 (\frac{3}{x})^{13} \frac{d}{d x} (\frac{3}{x})

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

= 14 (\frac{3}{x})^{13} (- \frac{3}{x ^{2}})

Simplify

14 (\frac{3}{x})^{13} (- \frac{3}{x ^{2}}) : - \frac{66961566}{x ^{15}}

= - \frac{66961566}{x ^{15}}

What is the derivative of (3/x ^{14}) ?
The derivative of (3/x ^{14}) is -(66961566)/(x^{15)}
What is the first derivative of (3/x ^{14}) ?
The first derivative of (3/x ^{14}) is -(66961566)/(x^{15)}