How do you differentiate $f (x) = 3 {(tan 4 x)}^{\frac{1}{2}}$ $f(x)=3(tan4x)^(1/2)$ using the chain rule?

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How do you differentiate $f (x) = 3 {(tan 4 x)}^{\frac{1}{2}}$ $f(x)=3(tan4x)^(1/2)$ using the chain rule?

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Answer 1 · 2017-04-06T03:46:55

$6 \cdot \frac{{sec}^{2} (4 x)}{{tan}^{\frac{1}{2}} (4 x)}$ $6*(sec^2(4x))/(tan^(1/2)(4x))$

Explanation:

$tan (4 x) = t$ $tan(4x)=t$
$\frac{d}{d t} (3 (t^{\frac{1}{2}})) = (\frac{3}{2}) \cdot (t^{- \frac{1}{2}})$ $d/dt(3(t^(1/2)))=(3/2)*(t^(-1/2))$
$\frac{d}{d x} (t) = 4 \cdot {sec}^{2} (4 x)$ $d/dx(t) = 4*sec^2(4x)$
combining them and converting t back we get
$6 \cdot \frac{{sec}^{2} (4 x)}{{tan}^{\frac{1}{2}} (4 x)}$ $6*(sec^2(4x))/(tan^(1/2)(4x))$

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How do you differentiate $f (x) = 3 {(tan 4 x)}^{\frac{1}{2}}$ $f(x)=3(tan4x)^(1/2)$ using the chain rule?

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Explanation:

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