Question

The function ?(?) = (sin ?)3 is a composition of two basic functions. Identify the outer function ? and the inner function ? to write the function of the form ?(?(?)), then use the chain rule to find the derivative ?′(?).

Answer #1

1) Create a function for which finding the first derivative
would involve a minimum of two of these following
rules:
1) Chain rule. 2) Product rule. 3) Quotient rule
State your function then find the equation of the tangent line
to the function at x=1. Leave values in exact form.

1) Write and answer a question that asks to solve an equation
that involves an logarithmic function. That is, your unknown must
be in a logarithmic function so that you must use inverse
operations (including exponentiation) to solve for it. Your
solution must include an exact answer, not a decimal
approximation.
2) Write and answer a question that asks you to find the
derivative of the sum or difference of at least three functions.
Your question and solution must demonstrate...

Prove that the composition of two linear fractional functions
is also a linear fractional function

2 If w =exp(x2y) and x
= sin(11t) and y = 21cos(-33t), find δw/δt in
two ways, once by plugging in, and once by the
chain rule.
3. Show why it is true that, if f(x, y) =
0 implicitly defines y as a function of x,
we can compute the derivative dy/dx as the negative of the
quotient of δf/δx and δf/δy.
4. Find the directional derivative of the function f(x,y) =
(x+1)4 cos(-5y) at the point
(0,1) in...

Set up a composition of two functions to solve the following
problem. 2. Courtney works at the local shoe store and receives
$150 a week plus 3% of all sales over $1000. This week her sales
were $3200. Find her commission using composition of two functions;
then find her total earnings for the week. f (x) = g (x) = Will you
use f(g(x)) or g(f(x)) to solve for the commission? Solve for the
commission using the composition of two...

post your conputation to this derivative:
F(x)=sin(tan(x))•cos(x)
using at least two of these: product rule, chain rule,
quotient rule

Find the directional derivative of the function at the given
point in the direction of the vector v.
f(x,y,z)= x2y3+2xz+yz3
(-2,1,-1) v= <1,-2,2>
Use the chain rule to find dz/dt. z=sin(x,y) x= scos(t)
y=2t+s3

1.
The Wronskian of the function x(t) = sin^3 t and an unknown
function y(t) is W (t) = sin^3 t. Find the general form of
y(t).

Identify the surface with parametrization x = 3 cos θ sin φ, y =
3 sin θ sin φ, z = cos φ where 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π. Hint: Find
an equation of the form F(x, y, z) = 0 for this surface by
eliminating θ and φ from the equations above. (b) Calculate a
parametrization for the tangent plane to the surface at (θ, φ) =
(π/3, π/4).

Use inverse trig functions to find the smallest two positive
solutions of sin(8x+2) = 0.7851 on [0,2π )

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