University:
Virtual High School
Course:
MCV4U | Calculus and Vectors
Academic year:

2023
Views:

19

Pages:

1
Author:

anon

MCV4U – Grade 12 Calculus & Vectors – Sinusoidal and Logarithmic Derivatives Sinusoidal and Logarithmic Derivatives Derivatives Sine and Cosine functions ● ● ● ● ● ● Derivative of y = sin x is y’ = cos x Derivative of y = cos x is y’ = -sin x Derivative of y = sin (f(x)) is y’ = cos (f(x)) * f’(x) Derivative of y = cos (f(x)) is y’ = -sinx (f(x)) * f’(x) Derivative of y = sin2 (f(x)) is y’ = 2 cos (f(x)) * f’(x) Derivative of y = cos2 (f(x)) is y’ = -2 sin (f(x)) * f’(x) Simple Harmonic Motion Trigonometry Application Problems ● 1st Derivative used to find velocities ● 2nd Derivatives used to find accelerations as well as max/min velocities ● To find period from its equation, it’s 360/k or 2 Pi / k for radians The number e ● The symbol e is defined as the limit when n -> infinity (1 + 1/n)n . The value is ~ 2.71 ● Rate of change of exponential function is also exponential ● Derivative of y = ex is y = ex (the same as original function) Natural Logarithm ● Lnx = logex ● The functions y = lnx and y = ex are inverses Derivatives of exponential functions ● ● ● ● The derivative of y = bx is y’ = bx * lnx The derivative of y = bf(x) is y’ = bf(x) * ln b * f’(x) The derivative of y = ef(x) is y’ = ef(x) * f’(x) You solve most logarithms by applying ln or log both sides and isolating the variable.