d/dx sin x = cos x, d/dx e^x = e^x, d/dx ln x = 1/x; the standard table of engineering calculus.
Standard results: (eˣ)'=eˣ, (ln x)'=1/x, (sin x)'=cos x, (cos x)'=-sin x, (tan x)'=sec²x, (aˣ)'=aˣ ln a, (arctan x)'=1/(1+x²). Memorising them speeds up analysis.
d/dt (V e^{-t/RC}) = -(V/RC) e^{-t/RC}, the capacitor discharge rate.
A short table of standard derivatives covers most of the calculus needed for signals, mechanics and thermodynamics.
d/dx sin x = cos x, d/dx e^x = e^x, d/dx ln x = 1/x; the standard table of engineering calculus.
A short table of standard derivatives covers most of the calculus needed for signals, mechanics and thermodynamics.
It is the unique function whose growth rate equals its value, which is why exponential growth and decay are so common in physical laws.
Zero, because a constant does not change with the input.
Typical applications include differentiating an exponential decay model for a capacitor voltage, finding the rate of change of a logarithmic sensor output and differentiating sine waves to get acceleration from displacement.
Study "Differentiation rules" first (topic 28 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Chain rule extends each entry. Hyperbolic functions have similar rules. Integrals are the reverse.
d/dt (V e^{-t/RC}) = -(V/RC) e^{-t/RC}, the capacitor discharge rate.
The next topic is "Applications of derivatives", which builds directly on this one.
It is classed as Beginner in Engineering Mathematics (topic 29 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.