What is the derivative of ${tan}^{3} (x^{4})$ $tan^3(x^4)$ ?

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What is the derivative of ${tan}^{3} (x^{4})$ $tan^3(x^4)$ ?

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Answer 1 · 2018-04-18T08:22:40

$\frac{d y}{d x} = 12 {tan}^{2} (x^{4}) {sec}^{2} (x^{4}) x^{3}$ $dy/dx=12tan^2(x^4)sec^2(x^4)x^3$

Explanation:

$y = {tan}^{3} (x^{4})$ $y=tan^3(x^4)$

$\frac{d y}{d x} = \frac{d}{d x} [{tan}^{3} (x^{4})] = 3 {tan}^{3 - 1} (x^{4}) \cdot \frac{d}{d x} [tan (x^{4})] = 3 {tan}^{2} (x^{4}) ({sec}^{2} (x^{4}) \frac{d}{d x} [x^{4}]) = 12 {tan}^{2} (x^{4}) {sec}^{2} (x^{4}) x^{3}$ $dy/dx=d/dx[tan^3(x^4)]=3tan^(3-1)(x^4)*d/dx[tan(x^4)]=3tan^2(x^4)(sec^2(x^4)d/dx[x^4])=12tan^2(x^4)sec^2(x^4)x^3$

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What is the derivative of ${tan}^{3} (x^{4})$ $tan^3(x^4)$ ?

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