What is the derivative of ${tan x}^{3}$ $tanx^3$ ?

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What is the derivative of ${tan x}^{3}$ $tanx^3$ ?

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Answer 1 · 2015-10-11T05:55:54

The derivative is $3 x^{2} \cdot {sec}^{2} (x^{3})$ $3x^2*sec^2(x^3)$ where $sec x$ $secx$ is the secant function

Explanation:

The derivative is

$d \frac{{tan x}^{3}}{d x} = d \frac{x^{3}}{d x} \cdot \frac{1}{{cos}^{2} (x^{3})} = 3 x^{2} \cdot (\frac{1}{{cos}^{2} (x^{3})}) = 3 x^{2} \cdot {sec}^{2} (x^{3})$ $d(tanx^3)/dx=d(x^3)/dx*1/cos^2(x^3)=3x^2*(1/cos^2(x^3))=3x^2*sec^2(x^3)$

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What is the derivative of ${tan x}^{3}$ $tanx^3$ ?

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