Question

Tentukan turunan dari beberapa fungsi trigonometri berikut

Answer 1

1. f(x) = cos x / (sinx +cosx)
u=cos x     u'=-sinx
v=sinx + cosx     v'=cosx-sinx

f(x)= u/v
f(x)= u'v-uv' / v²
f'(x)= -sinx(sinx + cosx) - cosx(cosx - sinx) / (sinx + cosx)²
f'(x)= -sin²x - sinx.cosx -cos²x + sinx.cosx / sin²x+2sinx.cosx+cos²x
f'(x)= -(sin²x+cos²x)+0 / (sin²x+cos²x)+2sinx.cosx
f'(x)= -1 / 1+2sinx.cosx

2. f(x) = cos x/x
u=cosx      u'=-sinx
v=x       v'=1
f'(x)= u'v-uv' / v²
f'(x)= -sinx(x) - cosx(1) / x²
f'(x)= -xsinx - cosx / x²

3. f(x)= x²+1 / xsinx
u=x²+1          u'=2x
v=xsinx       v'=u'v+uv'=(1)sinx+xcosx=sinx+xcosx
f'(x)= u'v-uv' / v²
=2x(xsinx)-(x²+1)(sinx+xcosx) / (xsinx)²
=2x²sinx - (x²sinx+x³cosx+sinx+xcosx) / x²sin²x
=2x²sinx - x²sinx - x³cosx - sinx - xcosx / x²sin²x
=x²sinx - x³cosx - sin x - xcosx / x²sinx.sinx
=-x³cosx - xcosx
= -cosx (x³+x)

jangan lupa jadiin jwaban terbaik