How do you differentiate $f (x) = sin x - \frac{1}{x cos x}$ $f(x)=sinx-1/(xcosx)$ using the sum rule?

Question

2317 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-07T19:29:39

$D_{x} f (x) = cos x + \frac{cos x + x sin x}{x^{2} {cos}^{2} x}$ $D_x f(x) = cos x + (cos x + x sin x)/(x^2 cos^2 x)$

$D_{x} f = cos x - D_{x} \frac{1}{u}$ $D_x f = cos x - D_x 1/u$ where $u = x cos x$ $u = x cos x$

$D_{x} f = cos x + \frac{1}{u^{2}} D_{x} (x cos x)$ $D_x f = cos x + 1/u^2 D_x (x cos x)$

$D_{x} f = cos x + \frac{1}{u^{2}} (1 cos x + x sin x)$ $D_x f = cos x + 1/u^2 (1 cos x + x sin x)$

How do you differentiate f(x)=sinx−1xcosxf(x)=sinx-1/(xcosx) using the sum rule?