CALCULUS II INTEGRALS AND DERIVATIVES
EXAM ANSWERED 2025-26 #15
Product Rule - correct answer f'(x)g(x)+f(x)g'(x)
Quotient Rule - correct answer g(x)f'(x)-f(x)g'(x)/g(x)^2
Chain Rule - correct answer f'[g(x)]g'(x)
Derivative of sin(x) - correct answer cos(x)
Derivative of cos(x) - correct answer -sin(x)
Derivative of tan(x) - correct answer (secx)^2
Derivative of sec(x) - correct answer sec(x)tan(x)
Derivative of csc(X) - correct answer -csc(x)cot(x)
Derivative of cot(x) - correct answer -(cscx)^2
Derivative of arcsin(x) - correct answer 1/√(1-x^2)
Derivative of arccos(x) - correct answer - 1/√(1-x^2)
Derivative of arctan(X) - correct answer 1/(1+x^2)
Derivative of arcsec(x) - correct answer 1/(|x|√(x)^2 -1)
Derivative of arccsc(x) - correct answer 1/(|x|√(x)^2 -1)
Derivative of arccot(x) - correct answer -1/(1+x^2)
Derivative of (a)^x - correct answer (a)^x ln(a)
Derivative of e^x - correct answer e^x
Derivative of ln(x) - correct answer 1/x where x>0
Derivative of ln|x| - correct answer 1/x where x≠0
(logₐ(x)) - correct answer 1/[xln(a)] , x > o
Intergral of cos(x)dx - correct answer sin(x)+c
EXAM ANSWERED 2025-26 #15
Product Rule - correct answer f'(x)g(x)+f(x)g'(x)
Quotient Rule - correct answer g(x)f'(x)-f(x)g'(x)/g(x)^2
Chain Rule - correct answer f'[g(x)]g'(x)
Derivative of sin(x) - correct answer cos(x)
Derivative of cos(x) - correct answer -sin(x)
Derivative of tan(x) - correct answer (secx)^2
Derivative of sec(x) - correct answer sec(x)tan(x)
Derivative of csc(X) - correct answer -csc(x)cot(x)
Derivative of cot(x) - correct answer -(cscx)^2
Derivative of arcsin(x) - correct answer 1/√(1-x^2)
Derivative of arccos(x) - correct answer - 1/√(1-x^2)
Derivative of arctan(X) - correct answer 1/(1+x^2)
Derivative of arcsec(x) - correct answer 1/(|x|√(x)^2 -1)
Derivative of arccsc(x) - correct answer 1/(|x|√(x)^2 -1)
Derivative of arccot(x) - correct answer -1/(1+x^2)
Derivative of (a)^x - correct answer (a)^x ln(a)
Derivative of e^x - correct answer e^x
Derivative of ln(x) - correct answer 1/x where x>0
Derivative of ln|x| - correct answer 1/x where x≠0
(logₐ(x)) - correct answer 1/[xln(a)] , x > o
Intergral of cos(x)dx - correct answer sin(x)+c
