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

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

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

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

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\frac{d}{d x} (\frac{x ^{3}}{cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{cos ( x )})

Simplify

\frac{x ^{3}}{cos ( x )} : x^{3} sec (x)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = sec (x)

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

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

d er i v a t i v e 2 - 3 x

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