Help me to understand the formal setup of the Chain Rule.

The procedure is shown using the easy example y=(5x^4+3x^2-2)^7.

Chain rule

Use Chain rule to solve: y=sin((ln(x^2+e^x)+2)^(1/2))^3.

Trigonometric Functions and Trigonometric Identities

I need to know the trigonometric functions and trigonometric identities.

Definition of derivative

Let f(x) be a continuous function of one variable. a) Give the definition of the derivative. b) Use this definition to find the derivative of f(x)=x^2+2x-5 c) Evaluate f'(2)

Calculus

1. A weather balloon is rising vertically at a constant rate of 4 ft/s directly above a straight and level road. When the balloon is 75 ft above the road, a car moving at 55 ft/s passes directly under the balloon. Based on this information find: a. the rate the distance between the balloon and the car is changing 3 sec after t ...continues

Finding the slope and other various characteristics of a line.

Given the points (3,7) and (-1, 3), find the slope of the line containing these 2 points, find the distance between these 2 points and find the midpoint.

Find the derivative of a quadratic polynomial.

Use the (limit) definition of the derivative to find the derivative of f(x)=3x^2-2x+1?

Working with initial value problems.

Solve the initial value problem: d²y/dx²= sec²x y(0)=0 and y'(0)=1

Geometric applications for calculus

I need an overview of geometric applications for calculus.

Understanding the concept of calculus.

What is calculus and how does it work?