What is the derivative of tan^4(5x) ?

The derivative of tan^4(5x) is 20tan^3(5x)sec^2(5x)

What is the first derivative of tan^4(5x) ?

The first derivative of tan^4(5x) is 20tan^3(5x)sec^2(5x)

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derivative

20 tan^{3} (5 x) sec^{2} (5 x)

Solution steps

\frac{d}{d x} (tan^{4} (5 x))

Apply the chain rule:

4 (tan (5 x))^{3} \frac{d}{d x} (tan (5 x))

= 4 (tan (5 x))^{3} \frac{d}{d x} (tan (5 x))

\frac{d}{d x} (tan (5 x)) = sec^{2} (5 x) \cdot 5

= 4 (tan (5 x))^{3} sec^{2} (5 x) \cdot 5

Simplify

= 20 tan^{3} (5 x) sec^{2} (5 x)

What is the derivative of tan^4(5x) ?
The derivative of tan^4(5x) is 20tan^3(5x)sec^2(5x)
What is the first derivative of tan^4(5x) ?
The first derivative of tan^4(5x) is 20tan^3(5x)sec^2(5x)