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Popular Calculus >

derivative of tan^4(2x-1^3)

Solution

\frac{d}{d x} (tan^{4} (2 x - 1)^{3})

Solution

24 tan^{11} (2 x - 1) sec^{2} (2 x - 1)

Solution steps

\frac{d}{d x} ((tan^{4} (2 x - 1))^{3})

Simplify

(tan^{4} (2 x - 1))^{3} : tan^{12} (2 x - 1)

= \frac{d}{d x} (tan^{12} (2 x - 1))

Apply the chain rule:

12 (tan (2 x - 1))^{11} \frac{d}{d x} (tan (2 x - 1))

= 12 (tan (2 x - 1))^{11} \frac{d}{d x} (tan (2 x - 1))

\frac{d}{d x} (tan (2 x - 1)) = sec^{2} (2 x - 1) \cdot 2

= 12 (tan (2 x - 1))^{11} sec^{2} (2 x - 1) \cdot 2

Simplify

= 24 tan^{11} (2 x - 1) sec^{2} (2 x - 1)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of tan^4(2x-1^3) ?
The derivative of tan^4(2x-1^3) is 24tan^{11}(2x-1)sec^2(2x-1)
What is the first derivative of tan^4(2x-1^3) ?
The first derivative of tan^4(2x-1^3) is 24tan^{11}(2x-1)sec^2(2x-1)