If f(x) = sin x, what is the 99th derivative of f(x)?

The 9750GII doesn't have symbolic capabilities so it can't give you a symbolic answer for this. It can evaluate it numerically at any point.

The derivative of sin(cos(x) dx is cos(cos(x))-sin(x).

The derivative of sin(cos(x)) dx is cos(cos(x))-sin(x). Unfortunately the fx-9850GII doesn't do symbolic differentiation so you'll have to get this result some other way. I cheated and used a calculator from another manufacturer, one that does do symbolic differentiation.

The differentiation rules for trigonometric functions you have been taught (ex: derivative of sin(x) is cos(x) ) are correct if the angle unit is in radians. If you use any other angle units (ex: degrees, grads) there will be a conversion factor :derivative of sin(ax) with respect to x is a.cos(ax).
Hope that helps

I do not know the program you installed, so I will skip the part.
As to the derivative of the sine function, your result is correct if the angle unit is degree.
d(sin(x))/dx = cos(x) is true only if the angle unit is the radian. In degrees, you would have a factor Pi/180 which is 0.174532925. I suggest you consult a calculus book to understand where that factor comes from.

Nevermind, i assume it's an acronym meaning with respect to x.
so the derivative of (sinx)x is: (cosx)(x) + (sinx)(1)
Simplified: xcosx + sinx

Use the rule for differentiating products of functions: ()' signifies derivative
(29*sin(2X)*sin(X))'= (29)'*sin(2X)*sin(X) +29* (sin(2X))'*sin(X) +29*sin(2X)*(sin(X))'
But

1. (29)'=0 derivative of a constant is zero
2. (sin(2X))'=cos(2X)*(2X)'=2*cos(2X)
3. (sin(X))'=cos(X)

Result is
(29*sin(2X)*sin(X))'= 29*2*cos(2X)*sin(X)+29*sin(2X)*cos(X)

You could also have cast your formula in the form
sin(2X)*sin(X)= 1/2[ cos(2X-X)-cos(2X+X)]=1/2[cos(X)-cos(3X)]
then calculated the derivative of
29/2*[cos(X)-cos(3X)]
which is
29/2*[-si(X) +3*sin(3X)]

The challenge for you is to prove that the two forms are equivalent
29*2*cos(2X)*sin(X)+29*sin(2X)*cos(X)=29/2*[-si(X) +3*sin(3X)]

Hello,

I assume that by anti-derivative you mean the integral. I believe that you can only calculate definite integrals with this calculator. A definite integral requires that you specify the function e.g ln(x), the variable, x, the numerical value of the lower limit, 0.5 and the numerical value of the upper limit , say 2.
Try this: INT(sin(x),x, 0, pi/2)
This calculator can only give numerical values of definite integrals. If you want to perform symbolic calculations, you shoul look towards some other, more sophisticated Casios Casio ClassPad 330, or the TI Voyage200PLT, or the TI89Titanium. etc.

Hope it helps

Hello,
Let us start wih the derivatives. To obtain the values of derivatives at points on a graph, you must set Derivative to ON
Press [AC/On] to trun calculator on. If you do not see the icons press [MENU], with arrows select [RUN] and press[EXE] . The screen clears.
Press [SHIFT][SETUP ] . The first few options must be set as follows
Mode : : Comp
Function Type : Y=
Draw Type : PLot
Derivative : ON This is the one to make derivatives visible
Angle : Rad unles you have to use degrees.
Coord : on if you want the x,y coordinates to be displayed
Grid : Off
Axes : ON to display x and y axes
Press [EXE] to save options. You are taken to [Run] screen.
Press [Menu] Play with arrows to select [GRAPH] and press [EXE]

You see a list Y1=, Y2= and so on
On the line Y1=, enter [SIN] [X,Theta, T] .
If function is complicated you may have to enter parentheses sin(X). When you finish to enter the functions you want to draw, hit [F6:Draw]
The graphs are displayed.
Press [F1:Trace] The trace function allows you to move cursor along the curve, while it displays the coordinates of the cursor. And since you set Derivative to ON, the trace displays also the value of the derivative of the curve at the position of the cursor.

There are other intersting tools, under [Sketch] and [G-solve ] such as minimum, maximum, tangente, inverse of the function drawn, integral under the curve, intercepts with the coordinates axes, etc. I will not spoil your fun by giving you the plot of the movie.

Hope it helps.

nderiv(nderiv(sin(x),x,x),x,2)