What is the derivative of sec^5(x^7+4x^6) ?

The derivative of sec^5(x^7+4x^6) is 30sec^{30}(x^7+4x)tan(x^7+4x)(7x^6+4)

What is the first derivative of sec^5(x^7+4x^6) ?

The first derivative of sec^5(x^7+4x^6) is 30sec^{30}(x^7+4x)tan(x^7+4x)(7x^6+4)

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\frac{d}{d x} (sec^{5} (x^{7} + 4 x)^{6})

30 sec^{30} (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

Solution steps

\frac{d}{d x} ((sec^{5} (x^{7} + 4 x))^{6})

Simplify

(sec^{5} (x^{7} + 4 x))^{6} : sec^{30} (x^{7} + 4 x)

= \frac{d}{d x} (sec^{30} (x^{7} + 4 x))

Apply the chain rule:

30 (sec (x^{7} + 4 x))^{29} \frac{d}{d x} (sec (x^{7} + 4 x))

= 30 (sec (x^{7} + 4 x))^{29} \frac{d}{d x} (sec (x^{7} + 4 x))

\frac{d}{d x} (sec (x^{7} + 4 x)) = sec (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

= 30 (sec (x^{7} + 4 x))^{29} sec (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

Simplify

30 sec^{29} (x^{7} + 4 x) sec (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4) : 30 sec^{30} (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

= 30 sec^{30} (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

What is the derivative of sec^5(x^7+4x^6) ?
The derivative of sec^5(x^7+4x^6) is 30sec^{30}(x^7+4x)tan(x^7+4x)(7x^6+4)
What is the first derivative of sec^5(x^7+4x^6) ?
The first derivative of sec^5(x^7+4x^6) is 30sec^{30}(x^7+4x)tan(x^7+4x)(7x^6+4)