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

The derivative of (s^3x)/(cos(x)) is 3s^2xsec(x)

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

The first derivative of (s^3x)/(cos(x)) is 3s^2xsec(x)

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derivative of

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

3 s^{2} x sec (x)

Solution steps

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

Simplify

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

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x sec (x) \cdot 3 s^{3 - 1}

Simplify

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

What is the derivative of (s^3x)/(cos(x)) ?
The derivative of (s^3x)/(cos(x)) is 3s^2xsec(x)
What is the first derivative of (s^3x)/(cos(x)) ?
The first derivative of (s^3x)/(cos(x)) is 3s^2xsec(x)