Chain rule/derivatives HW

What did I do wrong? 1. Find f'(x) when f(x)= 5x(sinx + cosx) My answer: cos(4x^2)- sin(6x^2)/(5x^2) 2. Find f'(x) when f(x)= ((x^3) + 4x + 4))^2 My answer: 6x^2(x^3 + 4x + 4) 3. Find f'(x) when f(x)= (3x + 8)^-3 My answer: -6(3x + 8) 4. Find f'(x) when f(x)= Sq root of (5x + 8) My answer: x/5x + 8 5. Find f'(x) when f( ...continues

Calculating rates of separation for related rates.

Northbound ship A leaves the harbour at 10:00 with a speed of 12km/h. Westbound ship B leaves the same harbour at 10:30 with a speed of 16km/h. (a) How fast are the ships separating at 11:30? (b) When is their rate of separation 18.86 km/h

Euclidean space

Compute the distance from a point b = (1, 0, 0, 1)^T to a line which passes through two points (0, 1, 1, 0)^T and (0, 1, 0, 2)^T. Here ^T denotes the operation of transposition, i.e. the points are represented by column-vectors instead of row-vectors.

Maxima: a)how many eggs are produced in one day. b)When are the eggs produced at the fastest rate

Eggs are produced at a rate of R(t)eggs per hour,where t=0 represents 12:00 midnight and R(t)(in thousands of eggs) is :- R(t)= -10cospi/12t+10 a)how many eggs are produced in one day. b)When are the eggs produced at the fastest rate c)A machine can produce eggs at a constant rate. At the end of 1 week the same ...continues

Limit of function f(x)=e^x

What happens when f(x)=e^x and x turns to infinity?

Trigonometric function: Find all solutions in radians. 4sin(squared)x-3=0

4sin^2 (x)-3=0

When to use the Chain Rule

The key is whether or not you are plugging the result of a function into another function. The idea is shown by contrasting the procedures for taking the derivatives of sin(x^2) and x^2*sin(x).

Definition and properties of exponential and logarithmic functions , formulae and example related to them.

Problems related to exponential and Logarithmic Functions

What is the equation of three bisecting solid rods centered at the origin?

Hello, What is the equation of three bisecting solid rods centered at the origin? Given 3 solid rods of length 3 and diameter 1. One rod is on the x-axis One rod is on the y-axis and One rod is on the z-axis Each is centered at the origin and is perpendicular to the other rods in each axis. Need equation in rectan ...continues

Explaination for derivatives

Explaination for derivatives related to exponential and logarithmic functions ,formulae used to solve them and solutions to some problems. All problems are in the solution file