How do you find the derivative of tanx/(1+sinx)?

1 Answer
Jim G.
Jul 3, 2017

((1+sinx)sec^2x-sinx)/(1+sinx)^2

Explanation:

"differentiate using the "color(blue)"quotient rule"

"given " f(x)=(g(x))/(h(x))" then"

f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"

g(x)=tanxrArrg'(x)=sec^2x

h(x)=1+sinxrarrh'(x)=cosx

rArrf'(x)=((1+sinx).sec^2x-tanxcosx)/(1+sinx)^2

color(white)(rArrf'(x))=((1+sinx)sec^2x-sinx)/(1+sinx)^2

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