Find {eq}f'(x) {/eq}: {eq}\displaystyle f(x) = \frac{x}{cos\ x^4} {/eq}

Question:

Find {eq}f'(x) {/eq}:

{eq}\displaystyle f(x) = \frac{x}{cos\ x^4} {/eq}

Quotient Rule:

The derivative of a fractional function of the form {eq}\dfrac{f(x)}{g(x)} {/eq} where {eq}g(x) \neq 0 {/eq} and both {eq}g(x) \ and \ f(x) {/eq} are differentiable functions is computed using the quotient rule formula of differentiation which is written below:

$$\dfrac{\mathrm{d} }{\mathrm{d} x}\left ( \dfrac{f(x)}{g(x)} \right )=\dfrac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}$$

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We have to find {eq}f'(x) {/eq}:

$$\displaystyle f(x) = \dfrac{x}{\cos\ x^4}$$

Differentiate the given function with respect to {eq}x {/eq}

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