How do you take the derivative of $y = {tan}^{2} (2 x)$ $y=tan^2(2x)$ ?

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How do you take the derivative of $y = {tan}^{2} (2 x)$ $y=tan^2(2x)$ ?

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Answer 1 · 2015-08-28T22:16:18

Use the power rule, the derivative of tangent and the chain rule (twice).

Explanation:

$y = {tan}^{2} (2 x)$ $y=tan^2(2x)$

First, remember the convention for trigonometric functions:

$y = {tan}^{2} (2 x) = {(tan (2 x))}^{2}$ $y=tan^2(2x) = (tan(2x))^2$

So the outermost function is the square. Use the power and chain rules to get:

$\frac{d y}{d x} = 2 (tan (2 x)) \cdot \frac{d}{d x} (tan (2 x))$ $dy/dx = 2(tan(2x)) * d/dx(tan(2x))$

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

$= 2 tan (2 x) \cdot {sec}^{2} (2 x) \cdot (2)$ $= 2tan(2x) * sec^2(2x) * (2)$

$= 4 tan (2 x) {sec}^{2} (2 x)$ $= 4tan(2x)sec^2(2x)$

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How do you take the derivative of $y = {tan}^{2} (2 x)$ $y=tan^2(2x)$ ?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you take the derivative of y=tan2(2x)y=tan^2(2x)?

1 Answer

Explanation:

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How do you take the derivative of $y = {tan}^{2} (2 x)$ $y=tan^2(2x)$ ?