Learn Calculus 1 - Become Expert on Calculus 1

Explore how limits apply to trigonometric functions, including small-angle behavior and key results as angles approach zero. Learn to evaluate common trig limits and understand their role in calculus fundamentals.

Prove that the limit as something approaches zero equals one by bounding areas with triangle and sector comparisons inside a circle.

Explore how to find the tangent line to a curve by using the slope of secant lines and the limit as delta x approaches zero.

Learn to compute the derivative from first principles using the limit as h approaches zero, applying the difference in function values to perform differentiation.

Apply first principles to differentiate y = sqrt(x) by rationalizing the numerator with a conjugate and simplifying to obtain the derivative 1/(2 sqrt(x)).

Differentiate sqrt(1+x) by introducing small increments, rewriting using algebraic forms to reveal a square difference, and taking the limit as increments approach zero.

Practice derivative calculations and expression simplifications in calculus 1, applying derivative rules to squared terms and expressions as shown in the exercise.

Apply differentiation to a polynomial function, using the derivative d/dx and power rules for squared and cubed terms, to obtain and verify the final derivative expression.

Practice exercise on differentiating a fraction-based function, applying algebraic rules and multiplication steps to find and simplify its derivative.

Learn how to apply the product rule to differentiate a product, using the derivative concept and practice exercise 3 to solidify understanding.

Master the chain rule overview by examining derivatives using limits, small increments, and the relationship between dy/dx and function increments.

This exercise demonstrates differentiating the function y = 2x^2 − 3x + 1, computing dy/dx, and using the derivative to simplify a division step in the problem.

Practice polynomial manipulation in this calculus 1 exercise by solving and simplifying expressions such as x^2+3 and 3x^2-1.

Derive the given function to obtain dy/dx, performing substitutions and handling cube and square terms to reach a simplified result.

learn the quotient rule overview by deriving the derivative of a ratio f(x)/g(x) using the limit definition and factoring to simplify.

This lecture demonstrates applying the power rule to differentiate expressions, including x^n and sqrt(x), noting that constants differentiate to zero and rewriting square roots as x^(1/2).

Differentiate c minus two x using the power rule, noting the derivative of a constant is zero, and conclude that the derivative is minus two.

Compute the derivative of the polynomial 3x^2 - 4x - 1 using the power rule, noting constants vanish, to obtain 6x - 4.

Explore the second derivative as the derivative of the first derivative, denoted d^2y/dx^2, and learn its notation as you differentiate again.

Explore how to calculate the second derivative and verify the first derivative, given y'' equals seven x squared plus six x plus five.