# Thread: How To Do Differentiation/Derivatives...?

1. ## How To Do Differentiation/Derivatives...?

#1 Suppose u and v are functions of x that are differentiable at x=0, and that u(0)=5,
u'(0)=-3,
v(0)=-1, and
v'(0)=2.

Find the values of the following derivatives at x=0.

a) (d/(dx))(uv)

b) (d/dx)(u/v)

c) (d/dx)(v/u)

d) (d/dx)(7v-2u)

For c and d, I do not know how to read this problem or approach it. I don't know what d stands for or what to do with the numbers surrounding it. Clueless.

#2 y=(x^2+3)/x

Find dy/dx by multiplying the factors first, then differentiating.

My work:

(I know how to do this be differentiating first, then multiplying the factors, but not the other way around...)

((x^2+3)(x) + (x^2+3)(x))/x^2
(x^3+3x+x^3+3x)/x^2
(3x^2+3+3x^2+3)/2x
(6x^2+6)/2x
6(x^2+1)/2x
3(x^2+1)/x
(3x^2+3)/x
3x + 3/x

How do you do these...?

2. Suppose u and v are functions of x that are differentiable at x=0, and that u(0)=5,
u'(0)=-3,
v(0)=-1, and
v'(0)=2.

Find the values of the following derivatives at x=0.

a) (d/(dx))(uv)

b) (d/dx)(u/v)

c) (d/dx)(v/u)

d) (d/dx)(7v-2u)

For c and d, I do not know how to read this problem or approach it. I don't know what d stands for or what to do with the numbers surrounding it. Clueless. Clueless?, then how did you get the correct solutions for (a) and (b) ? d/dx just means take the derivative w/r to x.

#2 y=(x^2+3)/x = x + (3/x) ... now take the derivative