What is the derivative of ((sec^2(x^3)/2)^4) ?

The derivative of ((sec^2(x^3)/2)^4) is (3x^2sec^8(x^3)tan(x^3))/2

What is the first derivative of ((sec^2(x^3)/2)^4) ?

The first derivative of ((sec^2(x^3)/2)^4) is (3x^2sec^8(x^3)tan(x^3))/2

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\frac{d}{d x} (\frac{sec ^{2} ( x ^{3} )}{2})^{4}

\frac{3 x ^{2} sec ^{8} ( x ^{3} ) tan ( x ^{3} )}{2}

Solution steps

\frac{d}{d x} (\frac{sec ^{2} ( x ^{3} )}{2})^{4}

Apply the chain rule:

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

= 4 (\frac{sec ^{2} ( x ^{3} )}{2})^{3} \frac{d}{d x} (\frac{sec ^{2} ( x ^{3} )}{2})

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

= 4 (\frac{sec ^{2} ( x ^{3} )}{2})^{3} \cdot 3 x^{2} sec^{2} (x^{3}) tan (x^{3})

Simplify

4 (\frac{sec ^{2} ( x ^{3} )}{2})^{3} \cdot 3 x^{2} sec^{2} (x^{3}) tan (x^{3}) : \frac{3 x ^{2} sec ^{8} ( x ^{3} ) tan ( x ^{3} )}{2}

= \frac{3 x ^{2} sec ^{8} ( x ^{3} ) tan ( x ^{3} )}{2}

\frac{d}{d x} (4 x (3 x - 2)^{5})

x \to 0 lim (x - 1)

\int (2 - x^{2})^{\frac{1}{2}} d x

y^{^{'}} = - y tan (t) + \frac{tan ( t )}{cos ( t )}

1 + 3 x, 3 \leq x \leq 9

What is the derivative of ((sec^2(x^3)/2)^4) ?
The derivative of ((sec^2(x^3)/2)^4) is (3x^2sec^8(x^3)tan(x^3))/2
What is the first derivative of ((sec^2(x^3)/2)^4) ?
The first derivative of ((sec^2(x^3)/2)^4) is (3x^2sec^8(x^3)tan(x^3))/2