Test: Differentiation I - Ambitious

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Question 1:   Find a derivative of the function   y=tg x 2 +3x
y'= 1 cos 2 x 2
y'= x cos 2 x 2 +3x
y'= 1 cos 2 x 2 +3x
y'= x+3 cos 2 x 2 +3x
Question 2:   Find a derivative of the function   y= e x 3 +5
y'= x 3 +5 e x 3 +5
y'= e x 3 +5
y'=3 x 2 e x 3 +5
y'= 3 x 2 +5 e x 3 +5
Question 3:   Find a derivative of the function   y= cos x
y'= 1 cos x
y'= sin x 2 cos x
y'= 1 2 cos x
y'= sin x 2 cos x
Question 4:   Find a derivative of the function   y=arcsin x 4 +2 x 2
y'= 1 1 x 4 +2 x 2
y'= 4 x 3 +x 1 x 8 4 x 6 +4 x 4
y'= 1 1 x 8 4 x 6 +4 x 4
y'= 4 x 3 1 x 8 4 x 6 +4 x 4
Question 5:   The function s is defined by:   s t = t 2 +t  ,  find the gradient of the function at the point   t 0 =5
v=11
v=23
v=5
v=1
Question 6:   The function s is defined by:   s t = t 3 2t  ,  find the gradient of the function at the point   t 0 =1
v=1
v=3
v=2
v=10
Question 7:   The function s is defined by:   s t = t 5 7t  ,  find the gradient of the function at the point   t 0 =2
v=5
v=25
v=66
v=20
Question 8:   At which point   f' x 0 >0 ?

x 0 =5
x 0 =4
x 0 =3
x 0 =0
Question 9:   At which point   f'( x 0 )=0 ?

x 0 =5
x 0 =2
x 0 =1
x 0 =3
Question 10:   At which point   f'( x 0 )<0 ?

x 0 =12
x 0 =11
x 0 =10
x 0 =8