What is the derivative of 7sec^5(pit-8) ?

The derivative of 7sec^5(pit-8) is 35pisec^5(pit-8)tan(pit-8)

What is the first derivative of 7sec^5(pit-8) ?

The first derivative of 7sec^5(pit-8) is 35pisec^5(pit-8)tan(pit-8)

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derivative of

7 sec^{5} (π t - 8)

35 π sec^{5} (π t - 8) tan (π t - 8)

Solution steps

\frac{d}{d t} (7 sec^{5} (π t - 8))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d t} (sec^{5} (π t - 8))

Apply the chain rule:

5 (sec (π t - 8))^{4} \frac{d}{d t} (sec (π t - 8))

= 5 (sec (π t - 8))^{4} \frac{d}{d t} (sec (π t - 8))

\frac{d}{d t} (sec (π t - 8)) = sec (π t - 8) tan (π t - 8) π

= 7 \cdot 5 (sec (π t - 8))^{4} sec (π t - 8) tan (π t - 8) π

Simplify

7 \cdot 5 sec^{4} (π t - 8) sec (π t - 8) tan (π t - 8) π : 35 π sec^{5} (π t - 8) tan (π t - 8)

= 35 π sec^{5} (π t - 8) tan (π t - 8)

What is the derivative of 7sec^5(pit-8) ?
The derivative of 7sec^5(pit-8) is 35pisec^5(pit-8)tan(pit-8)
What is the first derivative of 7sec^5(pit-8) ?
The first derivative of 7sec^5(pit-8) is 35pisec^5(pit-8)tan(pit-8)