math_calculus_differentiation_test_1Math(Calculus)testPaper-1 Time-1.5 hours
Questions
Marks
Score
Q-1 y=(3x2-9x+5)9finddydx
1
Q-2 y=sin-1(xx)finddydx
2
Q-3 ify=xcos(a+y)andcosa!=±1,thenproovethatdydx=cos2(a+y)sina
2
Q-4y=(x+1x) finddydx
2
Q-5 y=sinx finddydx
2
Q-6 y=cosx finddydx
2
Q-7 y=(x+1x)5 finddydx
2
Q-8 y=log5(log7x) finddydx
3
Q-9Iff(x)=xsinx , find f'(𝜋) using first principal
3
Q-10If y=tan-1x , where, xR,-𝜋2<y<𝜋2 then prove that dydx=11+x2
3
Q-11y=sin-1(2x1+x2) finddydx
3
Q-12y=x(x2x) finddydx
5
Q-13 y=xx+ax finddydx
4
Q-14 sin(x2+x) finddydx
2
Q-15 sin-1(x2-1) finddydx
3
Answer: 127(3x2-9x+5)8(2x-3) Answer: 232x1-x3 Answer: 3(not required) Answer: 4 (x2-1)x2x2x2+1 Answer: 5cosx2sinx Answer: 6-sinx2x Answer: 752xx(x-1)(x+1x)4 Answer: 81x.log5.logx Answer: 9-𝜋 Answer-10(not required) Answer: 1121+x2 Answer: 12y=x(x2x)x2x[logx][2(1+logx)+1xlogx] Answer: 13 xx(1+logx) Answer: 14 (2x+1)cos(x2+x) Answer: 15 22-x2