What is the derivative of (sec^2(x^3)/2) ?

The derivative of (sec^2(x^3)/2) is 3x^2sec^2(x^3)tan(x^3)

What is the first derivative of (sec^2(x^3)/2) ?

The first derivative of (sec^2(x^3)/2) is 3x^2sec^2(x^3)tan(x^3)

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

3 x^{2} sec^{2} (x^{3}) tan (x^{3})

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (sec^{2} (x^{3}))

Apply the chain rule:

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

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

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

= \frac{1}{2} \cdot 2 sec (x^{3}) sec (x^{3}) tan (x^{3}) \cdot 3 x^{2}

Simplify

\frac{1}{2} \cdot 2 sec (x^{3}) sec (x^{3}) tan (x^{3}) \cdot 3 x^{2} : 3 x^{2} sec^{2} (x^{3}) tan (x^{3})

= 3 x^{2} sec^{2} (x^{3}) tan (x^{3})

\frac{\partial}{\partial x} (x sin (5 x^{2} y))

\int - 2 sin^{5} (x) cos^{2} (x) d x

\frac{d}{d x} (1.795 x^{2})

t^{3} \frac{d x}{d t} + 3 t^{2} x = t

y = x^{2} e^{- x}, (1, \frac{1}{e})

What is the derivative of (sec^2(x^3)/2) ?
The derivative of (sec^2(x^3)/2) is 3x^2sec^2(x^3)tan(x^3)
What is the first derivative of (sec^2(x^3)/2) ?
The first derivative of (sec^2(x^3)/2) is 3x^2sec^2(x^3)tan(x^3)