MATH 2413 - EXAM 2 - CALCULUS
QUESTIONS WITH COMPLETE
SOLUTIONS
Definition of the number e - ANSWER-d/dx[eⁿ] = eⁿ (n = x)
Exponential Rule (any base) - ANSWER-d/dx[bⁿ] = bⁿ ln b (n = x)
Natural Log Rule - ANSWER-d/dx ln |x| = 1/x
Logarithmic Differentiation - ANSWER-d/dx (logₙx) = 1/x ln b (n = b)
Derivative of Sine - ANSWER-cos(x)
Derivative of Cosine - ANSWER--sin(x)
Derivative of Tangent - ANSWER-sec²x
Derivative of Cotangent - ANSWER--csc²x
Derivative of Cosecant - ANSWER--csc(x)cot(x)
Derivative of Secant - ANSWER-sec(x)tan(x)
Derivative of Inverse Sine - ANSWER-1/√1-x²
Derivative of Inverse Cosine - ANSWER--1/√1-x²
Derivative of Inverse Tangent - ANSWER-1/1+x²
Derivative of Inverse Cotangent - ANSWER--1/1+x²
Derivative of Inverse Cosecant - ANSWER--1/x√x²-1
Derivative of Inverse Secant - ANSWER-1/x√x²-1
The limit as x --> 0 sin x /
x = ? - ANSWER-1
The limit as x --> 0 cos(x) - 1 /
x = ? - ANSWER-0
Notation : cos^2 x = ? - ANSWER-(cos x)^2
QUESTIONS WITH COMPLETE
SOLUTIONS
Definition of the number e - ANSWER-d/dx[eⁿ] = eⁿ (n = x)
Exponential Rule (any base) - ANSWER-d/dx[bⁿ] = bⁿ ln b (n = x)
Natural Log Rule - ANSWER-d/dx ln |x| = 1/x
Logarithmic Differentiation - ANSWER-d/dx (logₙx) = 1/x ln b (n = b)
Derivative of Sine - ANSWER-cos(x)
Derivative of Cosine - ANSWER--sin(x)
Derivative of Tangent - ANSWER-sec²x
Derivative of Cotangent - ANSWER--csc²x
Derivative of Cosecant - ANSWER--csc(x)cot(x)
Derivative of Secant - ANSWER-sec(x)tan(x)
Derivative of Inverse Sine - ANSWER-1/√1-x²
Derivative of Inverse Cosine - ANSWER--1/√1-x²
Derivative of Inverse Tangent - ANSWER-1/1+x²
Derivative of Inverse Cotangent - ANSWER--1/1+x²
Derivative of Inverse Cosecant - ANSWER--1/x√x²-1
Derivative of Inverse Secant - ANSWER-1/x√x²-1
The limit as x --> 0 sin x /
x = ? - ANSWER-1
The limit as x --> 0 cos(x) - 1 /
x = ? - ANSWER-0
Notation : cos^2 x = ? - ANSWER-(cos x)^2
