Colourful Maths! Calculus for beginners

Calculate gradients on a curve using calculus and the derivative f'(x) as the gradient calculator. See examples with x values like -1, 0, and 3.

Discover the first principle of calculus by deriving the gradient of a line and the derivative of a curve using f(x), f(x+h), and the limit as h approaches zero.

Learn to graph calculus by locating where the gradient is positive, negative, or zero and its relation to the derivative above or below the x-axis, including asymptotes and infinity.

Investigate the first principles of calculus to derive derivatives, covering power rules, constants, and derivatives of x^n, ln x, sin x, cos x, and tan x, with gradient interpretations.

Explore graphing derivatives for parabolas, cubics, and quartics; learn that x squared gives 2x, x cubed gives 3x squared, and constants do not affect the derivative.

Explore calculus symbols and terms, review the derivative and gradient as rise and run, and connect dy/dx, d/dx, and differentials to small changes.

Master the chain rule by identifying outside vs inside functions, applying the derivative of the outside, then multiplying by the derivative of the inside, with worked examples.

Apply the product, quotient, and chain rules to differentiate functions, see how they relate, and solve practical problems with f(x) and g(x).

Identify stationary points by solving f'(x)=0, classify local and absolute maxima and minima, and distinguish points of inflection and stationary points of inflection.

Learn to identify stationary points by setting the derivative to zero and solving for x, yielding x = ±2, then classify as a maximum or minimum by derivative sign changes.

Learn to sketch any graph by using derivatives to locate stationary points and x-intercepts, then analyze end behavior with positive and negative test values.

Define antidifferentiation and show how it reverses differentiation, yielding y = x^2 + C. Explore dy/dx, the role of constants, and the integral that combines all dy/dx steps.

Learn to compute antiderivatives by reversing differentiation with the power rule, adding one to the exponent and dividing by the new power, including constants of integration and logs.

Tackle tougher antiderivatives by reviewing derivative notation, applying division and substitution, rewriting functions as integrals, and recovering the original function with a constant.

Compute approximate areas under a graph with rectangles, using left and right endpoint estimates and their average; heights come from f(x) and widths from end minus start over rectangles.

Learn how integration computes exact area under a curve by summing tiny rectangles from a to b, with dx approaching zero, and understand the difference between definite and indefinite integrals.

Learn to find exact area under a graph via integration, using the anti-derivative and definite integrals, handle negative areas by locating x-intercepts and applying absolute values to obtain total area.

Explore kinematics, the movement of objects, focusing on displacement, distance, velocity, and acceleration, and learn to read displacement-time graphs and compute average and instantaneous velocity.