Common Derivative Formulas You Must Memorize
This study pack covers the fundamental derivative formulas essential for Engineering Mathematics and Calculus.
Summary
This study pack covers the fundamental derivative formulas essential for Engineering Mathematics and Calculus. It begins with basic differentiation rules for constants, variables, and power functions. Key derivatives of trigonometric functions like sine, cosine, tangent, secant, cosecant, and cotangent are provided with their standard formulas. The pack also includes differentiation rules for exponential functions, including natural and general bases, as well as logarithmic functions with natural and arbitrary bases. Additionally, it presents primary differentiation techniques such as the Product Rule for derivatives of products, the Quotient Rule for derivatives of quotients, and the Chain Rule for composite functions. These formulas are critical for solving engineering problems and are commonly tested in board exams.
| Rule | Formula |
|---|---|
| Product | (uv)' = u'v + uv' |
| Quotient | (u/v)' = (u'v - uv') / v² |
| Chain | (f(g(x)))' = f'(g(x)) * g'(x) |
Common Misconceptions:
- Confusing the signs in derivatives of trigonometric functions, especially for cosine, cosecant, and cotangent.
- Misapplying the Chain Rule by neglecting to multiply by the derivative of the inner function.
- Incorrectly using the natural logarithm derivative formula for logarithms with different bases without adjusting by ln(a). This overview ensures a strong grasp of derivative formulas applicable in engineering contexts and problem-solving scenarios, strengthening analytical skills for calculus applications in engineering fields such as mechanical, electrical, and civil engineering.
🧠 Key Concepts
- Constant function derivative
- Power rule
- Trigonometric derivatives
- Exponential derivatives
- Logarithmic derivatives
- Product rule
- Quotient rule
- Chain rule
🧠 Quick Check
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What is the derivative of a constant function c with respect to x?
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Full Notes
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DERIVATIVE FORMULAS
These are the most common derivative formulas used in Engineering Math and Calculus.
Basic Rules: d/dx (c) = 0 d/dx (x) = 1 d/dx (x^n) = n*x^(n-1)
Trigonometric Functions: d/dx (sin x) = cos x d/dx (cos x) = -sin x d/dx (tan x) = sec^2 x d/dx (sec x) = sec x tan x d/dx (csc x) = -csc x cot x d/dx (cot x) = -csc^2 x
Exponential and Logarithmic: d/dx (e^x) = e^x d/dx (a^x) = a^x ln a d/dx (ln x) = 1/x d/dx (log_a x) = 1 / (x ln a)
Product Rule: d/dx (uv) = u'v + uv'
Quotient Rule: d/dx (u/v) = (u'v - uv') / v^2
Chain Rule: d/dx f(g(x)) = f'(g(x)) * g'(x)
These formulas are frequently used in board exams and problem solving.
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