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Popular >

derivative of tan^2(sin^4(t))

Solution

derivative of

tan^{2} (sin^{4} (t))

Solution

8 sin^{3} (t) sec^{2} (sin^{4} (t)) tan (sin^{4} (t)) cos (t)

Solution steps

\frac{d}{d t} (tan^{2} (sin^{4} (t)))

Apply the chain rule:

2 tan (sin^{4} (t)) \frac{d}{d t} (tan (sin^{4} (t)))

= 2 tan (sin^{4} (t)) \frac{d}{d t} (tan (sin^{4} (t)))

\frac{d}{d t} (tan (sin^{4} (t))) = sec^{2} (sin^{4} (t)) \cdot 4 sin^{3} (t) cos (t)

= 2 tan (sin^{4} (t)) sec^{2} (sin^{4} (t)) \cdot 4 sin^{3} (t) cos (t)

Simplify

= 8 sin^{3} (t) sec^{2} (sin^{4} (t)) tan (sin^{4} (t)) cos (t)

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Frequently Asked Questions (FAQ)

What is the derivative of tan^2(sin^4(t)) ?
The derivative of tan^2(sin^4(t)) is 8sin^3(t)sec^2(sin^4(t))tan(sin^4(t))cos(t)
What is the first derivative of tan^2(sin^4(t)) ?
The first derivative of tan^2(sin^4(t)) is 8sin^3(t)sec^2(sin^4(t))tan(sin^4(t))cos(t)