Question

find the derivative 4x^(3) tan(2x)

mainly how tan(2x) become sec^2(2x)

Answer #1

find the derivative of the function
f(x)=(4x-3)^5(2x^2+5x-8)^2

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

f(x) = (1 − x)tan−1(2x)
1.find the first and the second derivative of this
formula.
2. Find the Newton’s method formula for xn+1 in this
case.

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

Find the values of sin x, tan x, cot x, sec x, and csc x and cos
x given that cos(2x)=(3/5) and 3 π /2 < 2x <2 π

3.2) If a(t)=<-1/(t+1)^2, sec^3 t+ tan^2 t sec t,-t sin t+ 2
cos t- 2> represents the acceleration of a particle at time t
with v(0)=〈2,-1, 0〉 and r(0)=〈0, 2, 0〉 then find the distance from
the the particle to the plane 2x- 3y+z= 10 at t= 1
(ie Find the Distance from the particle to the Plane)

Consider the linearly independent set of vectors
B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4,
1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4)
in P4(R), does B form a basis for P4(R) and why?

1. Find the derivative of
f(x)= √4-sin(x)/3-cos(x)
2. Find the derivative of
1/(x^2-sec(8x^2-8))^2

Take derivative implicitly (tan(4u) + z^2)^5
What's the derivative of 4sin^3(x^7)
Sketch a rough graph of 3^x and use it to find the limit at both
inf and -inf. Expl how you know.

find the upper bound of the LTE (euler)
2x'+2/3 x = 4x^2
and the interval for t is [0,1].

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