Question

What is the derivative of y=sin^3(x)+sin(x^3) ?

Answer 1

What is

3sin^2(x)*cosx + cos(x^3)*3x^2

if one has cos^n (u^P) the derivative is

d/dx (sin^n (z)) where z=u^P then
= n cos^(n-1)(z)*-sin(z)*dz/dx

and dz/dx will be p*u^(p-1) du/dx and du/dx is depends on what u s.
the point is chain the derivative.

Answer 2

A container in the form of a right circular cone (vertex down) has a radius of 4m and height of 16m. If water is poured into the container at the constant rate of 16m^3/min, how fast is the water level rising when the water is 8m deep?
V=(pi/)(r^2)h

Answer 3

ddx(sin(x3)+(sin(x))3)
=ddx(sin(x3))+ddx((sin(x))3)
=3⋅(sin(x))2⋅ddx(sin(x))+cos(x3)⋅ddx(x3)
=3x2⋅cos(x3)+3⋅cos(x)⋅(sin(x))2