
Apply the power rule to differentiate polynomials by bringing down the exponent and lowering the power. Use the constant multiple rule for coefficients, and note constants have zero derivative.
Explore the power rule through more examples, differentiating functions with negative and fractional exponents, including x^(-9), x^(3/2), and sqrt(x), while keeping coefficients intact.
Apply the product rule to differentiate the product of two functions, using f'(x)g(x) + f(x)g'(x). See polynomial examples illustrating how the rates combine to give derivatives.
apply the quotient rule to differentiate f over g by computing (g f' - f g') / g^2, illustrated with top function 3x - 5 and bottom x^2 + 4.
Learn how to apply the chain rule to differentiate composite functions by differentiating the outer function and multiplying by the derivative of the inner function, with power rules and examples.
Learn derivatives of trigonometric functions—sin, cos, tan, cot, sec, csc—covering cos x, -sin x, sec^2 x, -csc^2 x, and product rule applications.
Utilize the chain rule to differentiate trig functions by identifying inside and outside functions, then multiply by the outside derivative; examples include sin(2x), tan(3x), and cot(πx).
Learn how to differentiate exponential functions, including base changes such as 2^x and 4^x, and apply the chain rule by multiplying the outside function’s derivative by the inside function’s derivative.
Learn to differentiate logarithmic functions, including natural logs with derivative 1/x and base-b logs with derivative 1/(x ln b), using the chain rule on inside functions.
Explore implicit differentiation by differentiating both sides with respect to x, applying the product rule as needed, and isolating dy/dx, using x^2 + y^2 = 9 as an example.
Learn logarithmic differentiation to differentiate products, quotients, and functions with roots by taking logs and using ln properties; apply it when base or exponent depends on x, as in x^x.
Videos: Every video covers a topic of differentiation. For every topic I solve some examples from simple to hard. I believe that we learn better with more exercises.
Quizzes: You can test your understanding and knowledge about a topic by taking a quiz ( All of them have complete solutions) . If you pass, congratulation. If not, you can review the videos again or look at the solutions of questions or ask me for help in the Q&A section.