What is the derivative of sec^3(5x) ?

The derivative of sec^3(5x) is 15sec^3(5x)tan(5x)

What is the first derivative of sec^3(5x) ?

The first derivative of sec^3(5x) is 15sec^3(5x)tan(5x)

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\frac{d}{d x} (sec^{3} (5 x))

15 sec^{3} (5 x) tan (5 x)

Solution steps

\frac{d}{d x} (sec^{3} (5 x))

Apply the chain rule:

3 (sec (5 x))^{2} \frac{d}{d x} (sec (5 x))

= 3 (sec (5 x))^{2} \frac{d}{d x} (sec (5 x))

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

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

Simplify

3 sec^{2} (5 x) sec (5 x) tan (5 x) \cdot 5 : 15 sec^{3} (5 x) tan (5 x)

= 15 sec^{3} (5 x) tan (5 x)

What is the derivative of sec^3(5x) ?
The derivative of sec^3(5x) is 15sec^3(5x)tan(5x)
What is the first derivative of sec^3(5x) ?
The first derivative of sec^3(5x) is 15sec^3(5x)tan(5x)