Universidade Tecnológica Federal do Paraná - UTFPR
Universidade Tecnológica Federal do Paraná - UTFPR
Universidade Tecnológica Federal do Paraná - UTFPR
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(m 1 ) f(x) = 5 tan 2x<br />
(e 2 ) y = 2x √ x 2 + 1<br />
(n 1 ) f(x) = (2x 3 − 3x) · (5 − x 2 ) 3<br />
(f 2 ) y = ex<br />
3<br />
1 + x 2<br />
(o 1 ) f(x) = −√ 3x − 5<br />
sin 2θ<br />
(g 2 ) y = e<br />
(p 1 ) y = e x2 +x+1<br />
(h 2 ) y = e mx cos nx<br />
(q 1 ) y = sin 2x · cos x<br />
(i 2 ) y = √ x cos √ x<br />
(r 1 ) y = (2x 2 − 4x + 1) 8<br />
(s 1 ) q = √ (x 2 + 1) 4<br />
(j 2 ) y =<br />
2r − r 2<br />
(2x + 1) 3 (3x − 1) 5<br />
( ) ( )<br />
3πt 3πt<br />
1<br />
(t 1 ) s = sin + cos<br />
(k 2 ) y =<br />
2<br />
2<br />
sin(x − sin(x))<br />
(u 1 ) h(x) = x tan(2 √ x) + 7<br />
(l 2 ) y = ln(cossec 5x)<br />
(v 1 ) r = sin(θ 2 ) cos(2θ)<br />
sec 2θ<br />
(m 2 ) y =<br />
(w 1 ) y = (4x + 3) 4 (x + 1) −3<br />
1 + tan 2θ<br />
(n<br />
(x 1 ) y = x tan −1 2 ) y = e cx (c sin x − cos x)<br />
(4x)<br />
(o<br />
(y 1 ) y = e cos x + cos(e x 2 ) y = ln(x 2 e x )<br />
)<br />
(z 1 ) y = cotg (3x 2 (p<br />
+ 5)<br />
2 ) y = sec(1 + x 2 )<br />
(a 2 ) y = ex<br />
(q 2 ) y = (1 − x −1 ) −1<br />
e −x + 1<br />
1<br />
(r 2 ) y = √ √<br />
(b 2 ) y = (x 4 − 3x 2 + 5) 3<br />
3<br />
(x + x)<br />
(c 2 ) y = cos(tan x)<br />
(s 2 ) y = √ sin √ x<br />
(d 2 ) y = √ 3x − 2<br />
(t 2x + 1 2 ) y = ln(sin x) − 1 2 sin2 x<br />
9. Derive utilizan<strong>do</strong> a derivada implícita:<br />
(a) xy 4 + x 2 y = x + 3y<br />
(b) x 2 cos y + sin 2y = xy<br />
(c) sin(xy) = x 2 − y<br />
(d) y = xe y − y − 1<br />
(e) y 2 + x 2 = 1<br />
(f) y 3 + yx 2 = sen x + 3y 2 x<br />
10. Encontre a derivada das seguintes funções:<br />
(a) y = 8 x<br />
cossec (x)<br />
(b) y = 3<br />
(c) y = x (x2 +1)<br />
(d) y = 7 x2 +2x<br />
(e) y = 3 x ln x<br />
(f) y = log 5 (1 + 2x)<br />
(g) y = (cos x) x<br />
(h) y = x sinh x 2<br />
(i) y = ln(cosh 3x)<br />
(j) y = cosh −1 (sinh x)<br />
tan πθ<br />
(k) y = 10<br />
(l) y = x · tanh −1 √ x<br />
11. Derive utilizan<strong>do</strong> a derivada inversa:<br />
(a) y = (arcsin 2x) 2<br />
(b) y = arctan(arcsin √ x)<br />
(c) y = √ x<br />
(d) y = ln x<br />
3