What is the derivative of 2sec^2(x^7) ?

The derivative of 2sec^2(x^7) is 28x^6sec^2(x^7)tan(x^7)

What is the first derivative of 2sec^2(x^7) ?

The first derivative of 2sec^2(x^7) is 28x^6sec^2(x^7)tan(x^7)

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\frac{d}{d x} (2 sec^{2} (x^{7}))

28 x^{6} sec^{2} (x^{7}) tan (x^{7})

Solution steps

\frac{d}{d x} (2 sec^{2} (x^{7}))

Take the constant out:

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

= 2 \frac{d}{d x} (sec^{2} (x^{7}))

Apply the chain rule:

2 sec (x^{7}) \frac{d}{d x} (sec (x^{7}))

= 2 sec (x^{7}) \frac{d}{d x} (sec (x^{7}))

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

= 2 \cdot 2 sec (x^{7}) sec (x^{7}) tan (x^{7}) \cdot 7 x^{6}

Simplify

2 \cdot 2 sec (x^{7}) sec (x^{7}) tan (x^{7}) \cdot 7 x^{6} : 28 x^{6} sec^{2} (x^{7}) tan (x^{7})

= 28 x^{6} sec^{2} (x^{7}) tan (x^{7})

What is the derivative of 2sec^2(x^7) ?
The derivative of 2sec^2(x^7) is 28x^6sec^2(x^7)tan(x^7)
What is the first derivative of 2sec^2(x^7) ?
The first derivative of 2sec^2(x^7) is 28x^6sec^2(x^7)tan(x^7)