What is the derivative of sec^9(2^x) ?

The derivative of sec^9(2^x) is 9ln(2)*2^xsec^9(2^x)tan(2^x)

What is the first derivative of sec^9(2^x) ?

The first derivative of sec^9(2^x) is 9ln(2)*2^xsec^9(2^x)tan(2^x)

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\frac{d}{d x} (sec^{9} (2^{x}))

9 ln (2) \cdot 2^{x} sec^{9} (2^{x}) tan (2^{x})

Solution steps

\frac{d}{d x} (sec^{9} (2^{x}))

Apply the chain rule:

9 (sec (2^{x}))^{8} \frac{d}{d x} (sec (2^{x}))

= 9 (sec (2^{x}))^{8} \frac{d}{d x} (sec (2^{x}))

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

= 9 (sec (2^{x}))^{8} sec (2^{x}) tan (2^{x}) \cdot 2^{x} ln (2)

Simplify

9 sec^{8} (2^{x}) sec (2^{x}) tan (2^{x}) \cdot 2^{x} ln (2) : 9 ln (2) \cdot 2^{x} sec^{9} (2^{x}) tan (2^{x})

= 9 ln (2) \cdot 2^{x} sec^{9} (2^{x}) tan (2^{x})

What is the derivative of sec^9(2^x) ?
The derivative of sec^9(2^x) is 9ln(2)*2^xsec^9(2^x)tan(2^x)
What is the first derivative of sec^9(2^x) ?
The first derivative of sec^9(2^x) is 9ln(2)*2^xsec^9(2^x)tan(2^x)