Differentiate the given function: f(w)=3w-\frac {\sec(w)}{1+9\tan(w)}


Differentiate the given function: {eq}f(w)=3w-\frac {\sec(w)}{1+9\tan(w)} {/eq}

Product rule and quotient rule

The product rule of differentiation is given by :

d(uv) = u dv + v du

The quotient rule of differentiation is given by :

{eq}\\\frac{d}{dx}(\frac{u}{v})=\frac{u'v-uv'}{v^2} {/eq}

Answer and Explanation:

{eq}f(w)=3w-\frac {\sec(w)}{1+9\tan(w)} {/eq}

Applying quotient rule for second term,

{eq}\\\frac{df}{dw}=3-\frac{(1+9\ tanw)\frac{d}{dw}(secw)-(secw)\frac{d}{dw}(1+9tanw)}{(1+9\ tanw)^2} \\\frac{df}{dw}=3-\frac{(1+9\ tanw)secw\ tanw-9sec^3w}{(1+9\ tanw)^2} {/eq}

Learn more about this topic:

Quotient Rule: Formula & Examples

from Division: Help & Review

Chapter 1 / Lesson 5

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